2014-2015学年高中毕业班阶段性测试(四)
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2014-2015学年高二上学期10月阶段测试地理试题本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分。
选择题答案用2B 铅笔涂在答题卡上,非选择题部分写在答题纸上。
考试结束后,将答题纸和答题卡一并交回。
第Ⅰ卷一、本卷共20个小题,每小题2分,共40分。
在每小题给出的四个选项中,只有一项是符合题目要求的。
读右面四幅图,回答1~2题。
1.①~④四地中位于北京(116°E,40°N)东南方向的是( ) A .① B .②C .③D .④2.四幅图中阴影部分所表示的经纬线方格,面积最大的是( ) A .甲 B .乙 C .丙 D .丁 读下面四幅等高线图,回答3~4题。
3.图中坡度最陡的是( )A .①B .②C .③D .④ 4.表示实地范围最大、内容最简略的是( )满分100分 考试时间50分钟A.①B.②C.③D.④读下面我国某区域水系图,回答5~6题。
5.图中河段水流较急的地点是()A.①B.②C.③D.④6.下列关于图示区域地理特征的描述,正确的是()①河流流量大,夏汛时间长②植被以温带落叶阔叶林为主③耕地以水田为主④河流无结冰现象,含沙量大⑤山区土壤以红壤为主,有机质含量低A.①②③B.②④⑤C.①③④D.①③⑤读右图,回答7~8题。
7.关于两条河流特征相同点的叙述,正确的是()A.冬半年有凌汛现象B.夏半年水量较丰富C.均为季节性积雪融水补给D.均自南向北注入大西洋8.关于甲、乙两图所示区域自然现象的叙述,正确的是()A.甲区域昼夜长短变化幅度大于乙区域B.甲区域对流层厚度大于乙区域C.两区域植被类型均以荒漠、草原为主D.两区域地形类型均以平原、高原为主下图为我国东部某地区等高线地形图。
读图,回答9~10题。
9.图中山峰与桥梁①的相对高度最有可能是( )A.450米B.650米C.750米D.850米10.对该地区的描述,正确的是( )A.河流的流向为自东北向西南 B.地势由北、南、东三面向西部倾斜C.②地夏季降水量大于③地 D.乙村易受泥石流的影响11.下列选项中,附近有世界最高山脉和最深海沟的一组板块界线是()A.印度洋板块——亚欧板块、太平洋板块——亚欧板块B.印度洋板块——亚欧板块、太平洋板块——美洲板块C.非洲板块——亚欧板块、太平洋板块——亚欧板块D.非洲板块——亚欧板块、太平洋板块——美洲板块读下图,回答第12~14题。
2014年下学期高二英语阶段性考试试卷命题人:韦健灵审核人:赵子卿第一部分:英语知识运用(共两节,满分40分)第一节:单项填空(共20小题;每小题1分,满分20分)从A、B、C、D四个选项中,选出最佳选项。
1. In China today, _______ car is becoming _____ popular means of transportation.A. a; theB. a; /C. the; theD. the; a2. –— It is unwise for some people to drive and talk on a cell phone.–— _______. It's very dangerous.A. That's greatB. Not reallyC. Good ideaD. I couldn't agree more3. Though having lived abroad for years, many Chinese still _______ the traditional customs.A. performB. possesC. observeD. support4Don’t wake Doctor Thompson up unless it is a real_______; he is too tired and needs a good rest.A. campaignB. emergencyC. argumentD. connection5. He spoke for a long time but his meaning did not ___________.A. come upB. come outC. come onD. come across6. ---John, can you help me fax the file?--- I would rather you _____ it by yourself.A.doB. will doC. didD. would do7. It is well-known that Madam Curie won two Nobel Prizes for her scientific _________.A. inspirationB. adventuresC. achievementsD. observation8. He sets us so difficult a problem_________ I couldn’t work out.A. thatB. asC. whichD. why9. The new stadium being built for the next Asian Games will be _______ the present one.A. as three times big asB. three times as big asC. as big as three timesD. as big three times as10. I'll give you your friend's home address, ______ I can be reached most evenings.A. whichB. whenC. whomD. where11. ________ in a heavy rain should be an unforgettable experience.A. CaughtB. CatchingC. Being caughtD. To catch12.Looking around the city, you’ll find many parks are _____________.A. worth being visitedB. worth a visitC. worthwhile being visitedD. worthy to a visit13.Lucy has a great sense of humour and always keeps her colleagues _____ with her stories.A. amusedB.amusingC.to amuseD.to be amused14.Scientists are convinced _____ the postive effect of laughter ____ physical and mental health.A.of;atB.by;inC. of;onD.on;at15.—Mr Black,what about my application?—Oh,I regret________you that it hasn’t been successful.A. tellingB. to tellC. having toldD. said16.He argued ______smoking, and insisted that it was ______ argument that smoking was harmfulto health.A. for; beyondB. against; overC. for; overD. against; beyond17.The president spoke at the business meeting for nearly an hour without _____ his notes.A.bringing upB.referring toC.looking forD.trying on.18.__________ you eat the correct foods ________ be able to keep fit and stay healthy.A.Only if; will youB. Only if; you willC.Unless; will youD. Unless; you will19.I saw Bob play the piano at John’s party and on that ______ he was simply brilliantA.sceneB.circumstanceC.occasionD.situation20.The factory used 65 percent of the raw materials, the rest of which _____ saved for otherpurposes.A. isB. areC. wasD. were第二节:完形填空(共20小题;每小题1分,满分20分)One fine afternoon I was walking along Fifth Avenue, ___ 21___ I remembered that it was necessary to buy a pair of socks. Why I wished to buy only one pair is ___22___. I turned into the first sock shop that ___23___ my eye, and a boy clerk who could not have been more than seventeen years old ___24___. "What can I do for you, sir?" "I wish to buy a pair of socks." His eyes were shining. There was a note of ___25___ in his voice. "Did you know that you had come into the finest place in the world to buy socks?" I had not been aware of that, as I entered the shop ___26___. "Come with me," said the boy, excitedly. I followed him to the back part of the shop, and he began to take down from the shelves box after box, ___27___ their contents for my enjoyment. "Hold on, young man, I am going to buy only one pair!" "I know that," said he, "but I want you to see ___28___ beautiful these are. Aren't they wonderful?"___29___ was on his face an expression of pleasure, ___30___ he were uncovering the mysteries of his religion. I became far ___31___ interested in him than in the socks. I looked at him in amazement. "My friend," said I, "if you can keep this up, if this is not ___32___ the enthusiasm that comes from having a new job, if you can keep up this enthusiasm and excitement day after day, in ten years you will own every ___33___ in the United States." My amazement ___34___ his pride and joy in salesmanship will be easily understood by all who read this article. In many shops the ___35___ has to wait for someone to serve him.21. A. while B. when C. as D. what22. A. unimportant B. unusual C. useless D. unnecessary23. A. kept B. shut C. took D. caught24. A. came about B. came across C. came forward D. came around25. A. anxiety B. shame C. panic D. excitement26. A. in particular B. in place C. by accident D. on purpose27. A. exchanging B. showing C. selling D. hiding28. A. how B. which C. that D. what29. A. There B. That C. One D. It30. A. although B. even if C. as if D. since31. A. much B. more C. less D. little32. A. mostly B. likely C. only D. hardly33. A. sock B. money C. joy D. store34. A. with B. at C. to D. on35. A. salesman B. passenger C. manager D. customerAnd when ___36___ some clerk does notice you, you are made to feel as if you were interrupting him.Either he is ___37___ in deep thought in which he hates to be disturbed or he is chatting with a girl clerk and you feel like ___38___ for "being too rude".He shows no interest either in you or in the goods he ___39___ to sell. Yet possibly the very clerk who is now so indifferent(冷漠的) began his career with hope and ___40___. The daily work was too much for him; the newness disappears slowly; his only pleasures were found outside of working hours; and he saw younger clerks who had more enthusiasm in their work promoted over him. He became sour. That was the last stage. His usefulness was over.36. A. firstly B. especially C. absolutely D. finally37. A. absorbed B. devoted C. busy D. attracted38. A. forgiving B. apologizing C. favoring D. approving39. A. paid B. is paid C. was paid D. pays40. A. content B. sympathy C. surprise D. enthusiasm第二部分:阅读理解(共20小题,每小题2分,满分40分)阅读下列短文,从每题所给的四个选项(A、B、C、D)中,选出最佳选项AArt museums are places where people can learn about various cultures. The increasingly popular "design museums" that are opening today, however, perform quite a different role. Unlike most art museums, the design museum shows objects that are easily found by the general public. These museums sometimes even place things like fridges and washing machines in the center of the hall.People have argued that design museums are often made use of as advertisements for new industrial technology. But their role is not simply a matter of sales—it is the honoring of excellently invented products. The difference between the window of a department store and the showcase in a design museum is that the first tries to sell you something, while the second tells you the success of a sale.One advantage of design museums is that they are places where people feel familiar with the exhibits. Unlike the average art museum visitors, design museum visitors seldom feel frightened or puzzled(困惑). This is partly because design museums clearly show how and why mass-produced products work and look as they do, and how design has improved the quality of our lives. Art museum exhibits, on the other hand, would most probably fill visitors with a feeling that there is something beyond their understanding.In recent years, several new design museums have opened their doors. Each of these museums has tried to satisfy the public's growing interest in the field with new ideas. London's Design Museum shows a collection of mass-produced objects from Zippo lighters to electric typewriters to a group of Italian fish-tins. The choices open to design museums seem far less strict than those to art museums, and visitors may also sense the humorous part of our society while walking around such exhibits as interesting and unusually attractive toys collected in our everyday life.41. Showcases in design museums are different from store windows because they ______.A. show more technologically advanced productsB. help increase the sales of productsC. show why the products have sold wellD. attract more people than store windows do42. The author believes that most design museum visitors ______.A. do not admire mass-produced productsB. are puzzled with technological exhibitsC. dislike exhibits in art museumsD. know the exhibits very well43. The best title for this passage is ______.A. The forms of design museumsB. The exhibits of design museumsC. The nature of design museumsD. The choices open to design museumsBFive or six years ago, I attended a lecture on the science of attention. A professor who conducts research over in the medical school was talking about attention blindness, the basic feature of the human brain that, when we concentrate on one task, causes us to miss just about everything else. Because we can't see what we can't see, our lecturer was determined to catch us in the act. He had us watch a video of six people tossing (投掷) basketballs back and forth, three in white shirts and three in black, and our task was to keep track only of the tosses among the people in white. The tape rolled, and everyone began counting.Everyone except me. I'm dyslexic (患阅读困难症的), and the moment I saw that tape with the confusing basketball tossers, I knew I wouldn't be able to keep track of their movements, so I let my mind wander. I became curious, though, when about 30 seconds into the tape, a gorilla (大猩猩) walked in among the players. She (we later learned a female student was in the gorilla suit) stared at the camera, beat her chest with her fist, and then went away while they continued passing the balls.When the tape stopped, the professor asked how many people had counted at least a dozen basketball tosses. Hands went up all over. He then asked who had counted 13, 14, and congratulated those who'd scored the perfect 15. Then he asked, "And who saw the gorilla?"I raised my hand and was surprised to discover I was the only person at my table and one of only three or four in the large room to do so. He'd set us up, trapping us in our own attention blindness. Yes, there had been a trick, but he wasn't the one who had played it on us. By concentrating so hard on counting, we had managed to miss the gorilla in the midst.Attention blindness is the fundamental organizing principle of the brain, and I believe that it presents us with a great opportunity. My take is different from that of many neuroscientists: Where they see the shortcomings of the individual, I sense an opportunity for cooperation. Fortunately, given the interactive(互动的) nature of most of our lives in the digital age, we have the tools to control our different forms of attention and take advantage of them.It's not easy to admit that everything we've learned about how to pay attention means that we've been missing everything else. It's not easy for us logical, intelligent, confident types to admit that the very key to our success — our ability to discover a problem and solve it, an achievement obtained in all those years in school and beyond — may be exactly what limits us. No one ever told us that our way of seeing left out everything else.44. Which of the following is true about the writer when the tape was played?A. Like everyone else, the writer was counting carefully.B. The writer had difficulty keeping track of the tossers' movements.C. The writer showed great curiosity about what the players were doing.D. The writer tried hard to stop her mind from wandering.45. What's the total number of basketball tosses by the players in white shirts in the video?A. 13.B. 14.C. 15.D. 30.46. Most of the people failed to notice the gorilla in the video because _____.A. they focused on the basketball tossing onlyB. they were trapped by the basketball playersC. they did not know what they were supposed to doD. they did not listen to the lecture carefully47. The word "take" (paragraph 5) most probably means _____.A. understandingB. impressionC. sceneD. preference48.In the writer's opinion, attention blindness ______.A. should be viewed as a shortcoming of the individualB. might be overcome if we can discover problems and solve themC. makes it possible for us to work together for a shared purposeD. helps us to become logical, intelligent and confident types of peopleCBelow are reviews for three books and two book series. Each has been read and loved by students across the country.The OutsidersThis book, first published in 1967. has become a classic for teens across the nation. It focuses on Ponyboy , who has been labeled all his life as a greaser. The greaser's opposing group is the " socs ". kids who have lots of money and can break any rules without getting in trouble. As the novel develops, S. E. Hinton allows the reader to see exactly how these labels affect teens in both the greaser and the soc group.If you've ever watched the movie The Outsiders, this story may sound familiar, as the movie was based on the book . The Outsiders gives teens a look into life in the 50's and 60's, offering timeless lessons that still apply to today's youth.Out of the Dus tAny student interested in the Great Depression and the Dust Bowl should read Out of the Dust by Karen Hesse. Hesse is able to capture the mood and spirit of this era through the use of poetry. The main character of the book, Billie Jo, is growing up in Oklahoma, the heart of the Dust Bowl. Through free verse poetry, Billie Jo narrates(讲述) her tale of poverty and survival during this difficult time.Out of the Dust is an excellent lesson in history . Due to the short length and writing style, the book is a quick but worthwhile read. By the end of the book, the reader is eager to start the story over again . Hesse is able to pack a lot of emotions and details into her short book , making the story very real and believable.The GiverThe Giver depicts a perfect society in which citizens experience no pain, have never felt fear,and life is completely under control. However, as the reader progresses through the story, it's easy to see that this community is far from utopia(乌托邦). Instead, through the experiences felt by the main character Jonas, the reader learns there is a missing from life in this world..During the Ceremony of the Twelves, each 12—year —old is assigned their life —long career in the community . Jonas is chosen to be the Receiver of Memories, a very special job assigned to oneperson at a time. When Jonas receives his training . he learns many truths about his community that change how he feels about his life, making him determined to do something to change it .The Giver is a good book for teens who enjoy science fiction and fantasy. The book makes you examine your own life, values, and beliefs, striving to find how you would define the perfect society.Anne of Green GablesThis eight-book series depicts the life of Anne Shirley, an orphan that is adopted in Prince Edward Island, Canada . The books are set in the 1800s to the 1900s, the last one taking place during World War I. Anne is a loveable spirit who has many misfortunes and laughable experiences when growing up and going to college.The Anne of Green Gables series is fun to read. creating a strong attachment to the reader and making the last book a bitter -sweet experience. Teenage girls who are looking for a female role model will love Anne Shirley.49. The greaser group may refer to those kids ______.A. who are poor in their lessons at schoolB. who are poor and often get into trouble for breaking rulesC. who go between the poor and the rich childrenD. who get along well with the soc group50. Which of the following is written in a poetic style?A. The Giver.B. The Outsiders.C. Out of the Dust.D. Anne of Green Gables.51. We can learn from The Giver that ______.A. everyone in the community can get a good jobB. Jonas is satisfied with his life in the communityC. people in the community live an imperfect lifeD. Jonas is loved by all the people in the community52. According to the passage, ______ may be chosen to be an example by teenage girls.A. Ponyboy B . Jonas. C. Billie Jo D. Anne ShirleyDIn the famous fairy tale, Snow White eats the Queen’s apple and falls victim to a curse; in Shakespeare’s novel, Romeo drinks the poison and dies; some ancient Chinese emperors took pills that contained mercury, believing that it would make them immortal, but they died afterward.Poison has long been an important ingredient in literature and history, and it seems to always be associated with evil, danger and death. But how much do you really know about poison?An exhibition, The Power of Poison, opened last month at the American Museum of Natural History in New York, intended to give the audience a more vivid understanding of poison. The exhibition will continue until Aug 2014, reported The New York Times.The museum tour starts in a rainforest setting, where you can see live examples of some of themost poisonous animals: caterpillars, frogs and spiders. Golden poison frogs, for instance, aren’t much bigger than a coin, but their skin is covered in a poison that can cut off the signaling power of your nerves, and a single frog has enough venom to kill 10 grown humans.The exhibition also features interactive activities. In an iPad-based game, visitors are presented with three puzzling illnesses and asked to identify the poisons based on symptoms. In one case, for example, a pet dog is found sick in a backyard and visitors have to figure out whether it was the toad (蟾蜍), the leaky batteries in the trash or the dirty pond water that did it.―Poisons can be bad for some things,‖ Michael Novacek, senior vice president of the museum,told NBC News. ―Yet they can also be good for others.‖This is what visitors learn from the last part of the exhibition, which displays how poisons can be used favorably by humans, including for medical treatment.The blood toxins of vampire bats, for example, can prevent blood from clotting (凝结), which may protect against strokes. A poisonous chemical found in the yew tree is effective against cancer, which is what led to the invention of a cancer-fighting drug called Taxol. One chemical in the venom of Gila monsters can lower the blood sugar of its victims, so it has been used to treat diabetes.The benefits from natural poisons are not limited to just medicine. Believe it or not, many substances that we regularly take in – chili, coffee and chocolate, etc. – owe their special flavors or stimulating effects to chemicals that plants make to poison insects.53. By mentioning Snow White and Romeo at the beginning of the story, the author intends to____________.A. show that poison has long been involved in literatureB. show that poison is always linked with evil and deathC. draw readers’ attention to the topic of the articleD. get readers to think of more examples of the use of poison in stories54. What is the main purpose of the exhibition The Power of Poison?A. To give people more in-depth knowledge about poison.B. To teach people how to handle poisonous animals.C. To inform people about which animals are the most poisonous.D. To show how poison has been used for medical treatment.55. Which of the following statements about the exhibition is TRUE according to the article?A. The exhibition will lead visitors to a real rainforest.B. Golden poison frogs are the most poisonous animals on display.C. Those who visit the exhibition can join in some iPad-based interactive games.D. Visitors can listen to lectures on recent studies of poisonous animals.EWhat is funny? The short answer is: Who knows? The joke that causes a burst of laughter from one listener might be met with a puzzled look from another.In general, you should avoid jokes at any business or social gathering where there are more than two people in your conversational group. If there are only two people — and they consist of you and your best friend — go ahead and tell it.Admittedly, a few people possess a perfect sense of timing, appropriateness, and joke delivery.You are probably not one of them. You might be quite funny and have many great jokes. Butthere's a place for jokes — over dinner with family, hiking with friends, but business or social affairs with colleagues and acquaintances(熟人) are not it. It takes a whole other level of joke-telling ability to put a joke into the more formal conversations.The best jokes come into the conversation so that by the time listeners realize a joke is in progress, the punchline that produces humour is being delivered — to their surprise and delight.Jokes don't translate well when you're in a group with mixed backgrounds: those whose first language is not English, those who might not understand a special term or an "in" expression, young people who wouldn't catch a reference to some bit of culture familiar to older people —and viceversa(反之亦然).Never joke about another person in the group — about their name, habits, hometown, profession, appearance, or past. It's not a question of whether the joke is cheery or appropriate. No one enjoys being singled out this way. When you are the subject of the joke, the laughter doesn't feel good no matter how hard you try to tell yourself they're not laughing at you. Because that's what it feels like.What do you say if you realize your joke upset someone? Apologize as briefly and as sincerely as you can, and hope that someone changes the subject. Try saying: "I'm sorry. I should have known better" or "I'm sorry. I wasn't thinking."What do you do if people don't get your joke or don't appear to find it as funny as you do? First, do not retell it, only louder this time, hoping the point of the joke will be seen. Second, don't try to push people to get it. People do not like people whose jokes they don't understand. They feel stupid and need to blame someone. If you want to leave with the goodwill of your listeners, say something to make them feel less foolish. You could say: "I don't know why I tell jokes when I'm so poor at it."The world needs laughter, and good humor is a success wherever it goes, so this caveat(告诫) about joke-telling is not meant to dampen high spirits or to advocate dull conversation. If you're a gifted story-teller and you know people love your jokes, go for it. We need your kind. The rest of us will save our jokes for family and close friends.56. According to the passage, it might be appropriate for you to tell a joke at a business or socialgathering if ______.A. the joke is well chosenB. you have complete confidence in your listeners' sense of humorC. only you and your best friend are involved in the conversationD. the audience consists of your colleagues and acquaintances57.Why do some jokes fail to work?A. Because the punchline is too long to catch.B. Because the joke-teller uses wrong words and expressions.C. Because the joke-teller and listeners don't share the same background knowledge.D. Because the jokes are not properly translated into the listeners' native language.58. How will people feel when they are joked about?A. They will feel happy if the joke is a pleasant one.B. They will be upset no matter what kind of joke it is.C. They will enjoy the joke when realizing that people are not laughing at them.D. They will panic because it makes them the center of attention.59. When people do not understand a joke they hear, they tend to ______.A. believe it's the joke-teller's faultB. get someone to retell the jokeC. ask for explanationD. say something foolish60. Which of the following best describes the writer's opinion on joke-telling?A. Nobody knows what makes a joke funny.B. We should not tell jokes unless we are asked to do so.C. Joke-telling is a very complex thing.D. Jokes should be told only to friends and family members.2014年下学期高二阶段性考试答题纸第一节单词拼写(共10小题,每小题1分,满分10分)61. We had a good rest in the s____________ of the trees.62. It is a good custom that the young have r__________ for the old in China.63. The speech he d____________ yesterday excited all the audience.64.The prisoner s___________ against the guard, but couldn’t escape.65.You are easy to get s___________ when staying on the beach in such a hot day.66.The business has e___________ into a big one.67. It was c________________ of him to underline the important sentences in the passage so thatothers could read it easily.68. You didn’t tell me you could sing so well---you’re very m___________.69. Those who are c___________ with what they have are more likely to be happy.70. I did not dare to speak aloud or even w_________ to Alison what was in my mind.第二节单句改错(共10小题,每小题1分,满分10分)格式错误不给分增加:在缺词处加一个漏字符号(∧),并在其下面写上该加的词。
湖南省新化一中2014-2015学年高二第四次阶段性测试试题理科数学命题:伍震斌 审题:卿梁松 满分:150分 时量:120分钟一、选择题(本大题共10小题,每小题5分,共50分. 在每小题给出的四个答案中,只有一项是符合题目要求的。
请将你认为正确的选项填在答题卡的相应的位置上。
)1、设集合2102x A x x ⎧+⎫=≤⎨⎬-⎩⎭,集合B 是()()ln 1f x x =-的定义域,则A B =( )DA. 112⎡⎤⎢⎥⎣⎦, B. (]1,2- C. ()()1112-,,D. ()12-, 【解析】122A x x ⎧⎫=-≤<⎨⎬⎩⎭,{}11B x x =-<<,A B ={}12x x -<<。
2、设变量x ,y 满足约束条件20201x y x y y +-≥⎧⎪--≤⎨⎪≥⎩,则目标函数2z x y =+的最小值为( )BA . 2B . 3C . 4D . 5【解析】画出可行域,如图所示.解方程组⎩⎪⎨⎪⎧x +y -2=0,y =1,得⎩⎪⎨⎪⎧x =1,y =1,即点A (1,1).当目标函数线过可行域内A 点时,目标函数有最小值,即z min =1×1+2×1=3。
3、如图,在平行六面体1111D C B A ABCD -中,M 为11C A 与11D B 的交点。
若AB a =,AD b =,1AA c =,则下列向量中与BM 相等的向量是( )CA. 1122a b c --+ B. 1122a b c ++ C. 1122a b c -++ D.1122a b c -+C1A 14、已知曲线x x y ln 342-=的一条切线的斜率为21,则切点的横坐标为( )A A. 3 B. 2 C. 1 D. 21【解析】x x y ln 342-=⇒13'2y x x =-0x >);令131'22y x x =-=,解得3x =。
河南天一大联考2015--2016学年高中毕业班阶段性测试(四)语文试题第Ⅰ卷阅读题甲必考题一、现代文阅读(9分,每小题3分)阅读下面的文字,完成1-3题。
直到目前为止,绝大多数对丝绸之路的研究是把丝绸之路作为一条实存的道路来研究,这当然是无可厚非的。
但是,也正是这种坚持对史实的研究,使得丝绸之路的另一项作用,即它在文学上所起的作用在很大程度上被忽视了,因为对于绝大多数人来说,丝绸之路还是一条传闻中的道路,一条存在与想象中的道路。
那些出于各种目的而四处流动的人,商人、旅行家、冒险者和传教僧,也许他们不是决定习性,但却是丝绸之路上文化传播最为活跃的因素。
他们在求取自己目的的同时,也把自己的信仰、途中的见闻以及关于其他地方的种种信息,沿途撒播,并随时吸取新的信息,以作新的谈资。
他们的谈论,由于目的不同而各有取舍,再加上口头传播的随意性以及临时的即兴表演,都使得信息本身的真实性得到削弱,而臆想的成分却在加强,于是千奇百怪的事情都可以在丝路上的某一时段某一点发生了。
总之,他们在传播神话的同时又在制造着神话,在取信于听众和取悦于观众上极尽所能地发挥着天赋。
以丝路道路的艰辛和古人对神的虔诚,我们不难想见,神们自然会与他们一道辗转流动,这使得丝绸之路又成为一条神话传播的大道。
但是,信任总是有底线的,在信息来源极度缺乏的地区,人们比较容易相信外来的传闻,而在丝绸之路这样一个各种信息汇聚的场所,却更容易培养出人们的怀疑精神。
特别是在同一个地方流传着关于同一个人或者同一件事的各种相互矛盾的传闻的时候,人们往往就面临选择了。
有趣的是,人们在做选择时的态度,他们更倾向选择那些和精神深处密切相关的事物作为应该相信的对象,并以此来印证和加固传统的信仰,也就是说,比起真相来,人们更容易选择他们一贯相信和愿意相信的事作为“事实”,而其他的事,哪怕是确曾发生,也会慢慢地被当做奇闻轶事来处理。
好在人们对奇闻轶事的兴趣,一点也不逊色他们对“真相”的追求。
2023—2024学年高中毕业班阶段性测试(四)地理考生注意:1.答题前,考生务必将自己的姓名、考生号填写在试卷和答题卡上,并将考生号条形码粘贴在答题卡上的指定位置。
2.回答选择题时,选出每小题答案后,用铅笔把答题卡对应题目的答案标号涂黑。
如需改动,用橡皮擦干净后,再选涂其他答案标号。
回答非选择题时,将答案写在答题卡上。
写在本试卷上无效。
3.考试结束后,将本试卷和答题卡一并交回。
一、选择题:本题共25小题,每小题2分,共50分。
在每小题给出的四个选项中,只有一项是符合题目要求的。
古浪县隶属甘肃省武威市,地处河西走廊东端,其境内南部为山林区,中部为农业区,北部为荒漠区。
图1示意古浪县产水服务(生态系统服务的重要组成部分,满足人类日常生产、生活用水需求)供需匹配类型的空间分布。
据此完成1~2题。
1.海子滩镇成为产水服务低供给区的主要影响因素是A.土壤B.植被C.天气D.河流2.横梁乡成为产水服务低需求区的主要原因是A.人口稀少B.农业发达C.交通便利D.工业集中湖北省钟祥市磷矿累计探明储量达7.44亿吨,是全国重要的磷化工基地,其重工业产值占工业总产值的70%。
2009年钟祥市被列入我国第二批资源枯竭型城市名单,2022年钟祥市入选国家级生态文明建设示范区。
据此完成3~4题。
3.钟祥市重工业发达的主要原因是A.市场广阔B.矿产资源丰富C.交通便利D.政府政策支持4.钟祥市转型过程中适宜发展的产业是A.边境贸易B.石油化工业C.房地产业D.生态旅游业2022年4月1日,《西安都市圈发展规划》正式获批,规划中提出,西安都市圈要构建“一核、两轴、多组团”的空间结构。
图2示意西安都市圈的范围。
据此完成5~6题。
5.西安都市圈的发展轴是①咸阳—西安—渭南一线②铜川—西安一线③渭南—商洛一线④庆阳—咸阳一线A.①②B.②③C.③④D.①④6.为提升西安市的辐射功能,西安都市圈适宜采取的举措是A.各市均加快建设机场B.推进城市间轨道交通建设C.加快将产业向西安集聚D.各城市产业趋同发展2023年6月11日,宁夏—湖南±800千伏特高压直流输电工程(俗称“宁电入湘”)正式开工建设,这是我国首条以输送新能源为主的电力外送大通道,是我国“西电东送”的重要组成部分。
天一大联考(原豫东、豫北十所名校联考)2014-2015学年高中毕业班阶段性测试(三)安阳一中郸城一高扶沟高中鹤壁高中淮阳中学济源一中开封高中灵宝一高洛阳一高林州一中内黄一中南阳一中南阳五中平顶山一中濮阳一高商丘一高太康一高温县一中新乡一中夏邑高中信阳高中(学校名称按其拼音首字母顺序排列)本试题卷分第1卷(阅读题)和第Ⅱ卷(表达题)两部分。
考生作答时,将答案答在答题卡上(答题注意事项见答题卡),在本试题卷上答题无效。
考试结束后,将本试题卷和答题卡一并交回。
第1卷阅读题必考题一、现代文阅读(9分,每小题3分)阅读下面的文字,完成1~3题。
技术与人的关系,是一个不断演变的历史过程。
在手工劳动中,原始技术同劳动者不可分离。
手工劳动的技术,是最原始的技术,表现为劳动者的技能,即手控制手工工具的能力,亦称手工技能。
这种原始技术本质上是人的体能。
人的体能有两种功能:一是改变物体状态的能力,即体力。
二是控制物体的能力,在手工劳动中就表现为控制手工工具的能力。
这就是最早的技术——体技或手技。
所有的技术都是人对自己的超越。
人的双手的动作不准确、不精确,而手工技术追求的就是一准二精。
这种准确性和精确性的提高,不是通过工具,而是通过劳动者的苦练得来的。
“熟能生巧”,这“巧”是手之巧,靠的是熟练。
手工技能是由双手的动作的准和精表现出来的,它在一定程度上超越了人的生理局限,提高了人的生理功能,是“生理性技术”。
手工技能很难用语言文字来表达,它本身也不是知识,也不需要知识作为前提条件。
它只可意会,不可言传。
别人要学习这种技能,主要靠动作的模仿和用心去领悟。
这种技术的传授必须面对面进行。
这种手工技能是劳动者的身体所具有的,存在于劳动者体内,离开了劳动者的双手,这种技能就不再存在。
这种技能与其说是“社会的”,不如说是个人的,它不可能在空间上大规模传播,也不可能在时间上世代相传。
由于人具有高度的个性,所以手工技能也具有一定的个性。
2022—2023学年高中毕业班阶段性测试(四)文科数学一、选择题:本题共12小题,每小题5分,共60分.在每小题给出的四个选项中,只有一项是符合题目要求的.1.已知集合{}0A x x =≥,{}1B x x =≠,则A B ⋂=( ) A .{}0x x ≥B .{}1x x >C .{}011x x x ≤<>或D .{}01x x ≤<2.若()12i 112i z +=+,则z =( ) A .34i +B .34i -C .43i +D .43i -3.已知函数()f x 在R 上的导函数为()f x ',则“()00f x '=”是“0x 是()f x 的极值点”的( ) A .充分必要条件 B .既不充分也不必要条件 C .充分不必要条件D .必要不充分条件4.已知向量a ,b 的夹角为56π,且3a =,1b =,则2a b +=( )A .1B C .2D5.已知函数()f x 是奇函数,且当0x ≥时,()f x x =,则()4f -=( )A .4-B .2-C .2D .46.若1cos 2cos sin sin 2cos θθθθθ--=,则tan 4πθ⎛⎫+= ⎪⎝⎭( )A .3B .2C D .17.已知A 为抛物线C :24y x =上在第一象限内的一个动点,()1,0M -,O 为坐标原点,F 为C 的焦点,若tan 3AMO ∠=,则直线AF 斜率的绝对值为( )A .2B .C .13D .438.若棱长均相等的正三棱柱的体积为O 的表面上,则球O 的表面积为( ) A .283π B .1129π C .6πD .1123π 9.下表为某外来生物物种入侵某河流生态后的前3个月繁殖数量y (单位:百只)的数据,通过相关理论进行分析,知可用回归模型()1aty ea +=∈R 对y 与t 的关系进行拟合,则根据该回归模型,预测第6个月该物种的繁殖数量为( )第t 个月 1 2 3繁殖数量y1.4e2.2e2.4eA .3e 百只 B . 3.5e百只 C .4e 百只D . 4.5e百只10.函数()31123f x x x=+-的零点个数为( ) A .1B .2C .3D .411.在ABC △中,角A ,B ,C 的对边分别为a ,b ,c ,若2A B =,则3a cb-的取值范围为( ) A .(]3,4B .712,35⎛⎤⎥⎝⎦ C .133,4⎛⎤⎥⎝⎦D .(]2,512.已知双曲线()222210,0x y a b a b -=>>的左顶点为A ,点0,2b B ⎛⎫⎪⎝⎭,直线AB 与双曲线的两条渐近线分别交于P ,Q 两点,若线段PQ 的垂直平分线经过双曲线的右顶点,则双曲线的离心率为( ) A .2B .3C .52D .233二、填空题:本题共4小题,每小题5分,共20分.13.在区间[]2,3-上随机取一个数x ,则1x >的概率为______.14.已知实数x ,y 满足约束条件10,10,240,x y x x y -+≤⎧⎪+≥⎨⎪-+≥⎩则3z x y =+的最大值为______.15.已知函数()()cos ,0,2f x A x A πωϕωϕ⎛⎫=+>≤⎪⎝⎭的部分图象如图所示,将()f x 的图象向右平移4T(T 为()f x 的最小正周期)个单位长度得到()g x 的图象,则()0g =______.16.已知圆锥内有一个内接圆柱,圆柱的底面在圆锥的底面内,当圆柱与圆锥体积之比最大时,圆柱与圆锥的底面半径之比为______.三、解答题:共70分.解答应写出文字说明,证明过程或演算步骤.第17~21题为必考题,每个试题考生都必须作答.第22,23题为选考题,考生根据要求作答.(一)必考题:共60分.17.(12分)已知数列{}n a 的前n 项和252n n nS -=.(Ⅰ)求{}n a 的通项公式; (Ⅱ)设10,10,2,10,n n n a n b b n -≤⎧=⎨>⎩求数列{}n b 的前30项和.18.(12分) 某超市为改善某产品的销售状况并制订销售策略,统计了过去100天该产品的日销售收入(单位:万元)并分成六组制成如图所示的频率分布直方图.(Ⅰ)求a 的值并估计过去100天该产品的日销售收入的平均值x ;(同一区间数据以中点值作代表)(Ⅱ)该超市过去100天中有30天将该商品降价销售,在该商品降价的30天中有18天该产品的日销售收入不低于0.6万元,判断能否有97.5%的把握认为该商品的日销售收入不低于0.6万元与该日是否降价有关.附:()()()()()22n ad bc K a b c d a c b d -=++++,其中n a b c d =+++.()20P K k ≥0.050 0.025 0.010 0k3.8415.0246.63519.(12分)如图,在四棱锥P -ABCD 中,PC BC ⊥,PA PB =,APC BPC ∠=∠. (Ⅰ)证明:PC AD ⊥;(Ⅱ)若AB CD ∥,PD AD ⊥,3PC =,且点C 到平面P AB 的距离为62,求AD 的长.20.(12分) 已知函数()32213f x x x ax =-+-,a ∈R . (Ⅰ)若曲线()y f x =在点()0,1-处的切线斜率为4-,求()f x 的单调区间;(Ⅱ)若存在唯一的()00,2x ∈,满足()()01f x f =-,求a 的取值范围. 21.(12分)已知椭圆()2222:10x y C a b a b +=>>的离心率为23,且3⎫⎪⎪⎭为C 上一点. (Ⅰ)求C 的标准方程;(Ⅱ)点A ,B 分别为C 的左、右顶点,M ,N 为C 上异于A ,B 的两点,直线MN 不与坐标轴平行且不过坐标原点O ,点M 关于原点O 的对称点为M ',若直线AM '与直线BN 相交于点P ,直线OP 与直线MN 相交于点Q ,证明:点Q 位于定直线上.(二)选考题:共10分.请考生在第22,23题中任选一题作答,如果多做,则按所做的第一题计分. 22.[选修4-4:坐标系与参数方程](10分)在直角坐标系xOy 中,曲线C 的参数方程为2224,4824t x t t y t ⎧=⎪⎪+⎨-⎪=⎪+⎩(t 为参数),以坐标原点O 为极点,x 轴正半轴为极轴建立极坐标系,直线l 的极坐标方程为cos sin 4ρθρθ+=. (Ⅰ)求曲线C 的普通方程;(Ⅱ)若P 为C 上一动点,求P 到l 的距离的取值范围. 23.[选修4-5:不等式选讲](10分) 已知函数()112222f x x x =++-. (Ⅰ)求不等式()3f x <的解集;(Ⅱ)设()f x 的最小值为M ,若正实数a ,b 满足221a b M a b +=++,证明:32a b +≥.2022—2023学年高中毕业班阶段性测试(四)文科数学·答案一、选择题:本题共12小题,每小题5分,共60分.1.答案 C命题意图 本题考查集合的交运算. 解析 {}011A B x x x ⋂=≤<>或. 2.答案 A命题意图 本题考查复数的四则运算. 解析 ()()()()112i 12i 112i 1520i34i 12i 12i 12i 5z +-+-====-++-,则34i z =+.3.答案 D命题意图 本题考查极值点的概念以及充分必要条件的判断.解析 由极值点的定义,若0x 为()f x 的极值点,则有()00f x '=,而由()00f x '=不一定推得0x 为()f x 的极值点,例如()3f x x =,故“()00f x '=”是“0x 是()f x 的极值点”的必要不充分条件. 4.答案 A命题意图 本题考查平面向量的运算. 解析 ()22222443431ab a ba ab b +=+=+⋅+=+⨯=. 5.答案 C命题意图 本题考查奇函数的概念.解析 因为()f x 是奇函数,所以()()44f f -=-,又()442f ==-,所以()42f -=. 6.答案 A命题意图 本题考查三角恒等变换.解析 由题意()2112sin 1tan 2sin cos θθθθ--=-,即1tan 2θ=,1tantan 142tan 3141tan tan 142πθπθπθ++⎛⎫+===⎪⎝⎭--. 7.答案B命题意图 本题考查抛物线的性质.解析设211,4y A y ⎛⎫ ⎪⎝⎭,1210tan 314AMy AMO k y -∠===+,解得1y 或1y =12A ⎛ ⎝或(2,A ,又()1,0F ,所以0112AF k ==--AF k ==AF k =. 8.答案 D命题意图 本题考查三棱柱的外接球.解析 设该正三棱柱棱长为x ,底面三角形的外接圆半径为r ,则21sin 602x x ︒⋅⋅=,∴4x =,则r =O 半径为R ,则22216284233x R r ⎛⎫=+=+=⎪⎝⎭,228112=4=4=33S R πππ⨯表. 9.答案 C命题意图 本题考查回归分析. 解析 由题意,1aty e+=两边取自然对数得ln 1y at =+,令ln u y =,则1u at =+.()1231ln ln ln 23u y y y =++⨯=,()123123t t t t =++⨯=,∵回归直线必过样本点的中心,∴221a =+,得12a =,∴12tu =+,则12t y e +=.当6t =时,4y e =.10.答案 B命题意图 本题考查函数零点问题.解析 易知()f x 的定义域为{}0x x ≠,()422211x f x x x x -'=-=,令()0f x '<,解得10x -<<或01x <<,∴()f x 在()1,0-和()0,1上单调递减,令()0f x '>,解得1x <-或1x >,∴()f x 在(),1-∞-和()1,+∞上单调递增.当1x =-时,()f x 取得极大值()10103f -=-<,易知()f x 在(),0-∞上没有零点;当1x =时,()f x 取得极小值()2103f =-<,且1820381f ⎛⎫=> ⎪⎝⎭,()7206f =>,可知()f x 在()0,+∞上有2个零点.综上所述,()f x 的零点个数为2. 11.答案 C命题意图 本题考查解三角形.解析 ∵2A B =,∴sin sin 22sin cos A B B B ==且0,3B π⎛⎫∈ ⎪⎝⎭,()3sin sin sin33sin 4sin C A B B B B =+==-,由正弦定理可得333sin sin 6sin cos 3sin 4sin sin sin a c A C B B B Bb B B---+==()226cos 41cos 34cos 6cos 1B B B B =+--=-++,令1cos ,12B t ⎛⎫=∈ ⎪⎝⎭,则23461a c t t b -=-++,由二次函数性质知2134613,4t t ⎛⎤-++∈ ⎥⎝⎦,∴3133,4a c b -⎛⎤∈ ⎥⎝⎦. 12.答案 B命题意图 本题考查双曲线的性质和离心率的求法. 解析 不妨设点P 在直线b y x a =上,由题可知(),0A a -,∴2AB b k a =,∴:22AB b bl y x a =+,由,22,b by x a b y x a⎧=+⎪⎪⎨⎪=⎪⎩得,,P P x a y b =⎧⎨=⎩∴(),P a b ,同理,33a b Q ⎛⎫- ⎪⎝⎭,∴PQ 的中点为2,33a b ⎛⎫ ⎪⎝⎭,PQ 的垂直平分线方程为2233b a a y x b ⎛⎫-=-- ⎪⎝⎭,将0,y x a=⎧⎨=⎩代入整理得222b a =,则e ==二、填空题:本题共4小题,每小题5分,共20分. 13.答案35命题意图 本题考查几何概型的计算.解析 在区间[]2,3-上随机取一个数x ,若1x >,则[)(]2,11,3x ∈--⋃,所以1x >的概率为()()12313325-++-=+.14.答案 9命题意图 本题考查线性规划.解析 根据不等式组作出可行域如图中阴影部分所示,当目标函数表示的直线经过点()2,3时,3z x y =+取得最大值9.15.答案 3命题意图 本题考查三角函数的图象和性质. 解析 由图可知2A =,22362T πππ=-=,∴T π=,22πωπ==.由()226k K πϕπ⨯+=∈Z ,及2πϕ≤,得3πϕ=-,∴()2cos 23f x x π⎛⎫=-⎪⎝⎭,∴()52cos 22cos 2436g x x x πππ⎡⎤⎛⎫⎛⎫=--=- ⎪ ⎪⎢⎥⎝⎭⎝⎭⎣⎦,∴()502cos36g π==- 16.答案23命题意图 本题考查导数的应用.解析 设圆锥的底面半径为R ,圆锥的轴截面为等腰三角形,底边长为2R ,设其底角为α,则圆锥的高为tan R α,圆锥的体积为3tan 3R πα.设圆锥内接圆柱的底面半径为r ,高为h ,则tan tan r R hR R αα-=,即()tan h R r α=-,则圆柱的体积为()()2223tan tan r h r R r Rr r ππαπα=-=-,()0,r R ∈.圆柱与圆锥体积之比为23233r r R R ⎛⎫- ⎪⎝⎭,设()01r t t R =<<,()23f t t t =-,则()()22323f t t t t t '=-=-.由()0f t '=,得23t =,当203t <<时,()0f t '>,当213t <<时,()0f t '<,所以当23t =时,()f t 取得最大值,即圆柱与圆锥体积之比最大,此时23r R =.三、解答题:共70分.解答应写出文字说明,证明过程或演算步骤. 17.命题意图 本题考查数列求通项和数列求和. 解析(Ⅰ)111522a S -===-, 当2n ≥时,有252n n n S -=,()()211512n n n S ----=,两式相减得()()()2215151322n a n n n n n n ⎡⎤=---+-=-≥⎣⎦,当1n =时,12a =-符合上式,故3n a n =-.(Ⅱ)设数列{}n b 的前n 项和为n T ,则()()()301210111220212230T b b b b b b b b b =++⋅⋅⋅++++⋅⋅⋅++++⋅⋅⋅+. 由题意得1210121010b b b a a a S ++⋅⋅⋅+=++⋅⋅⋅+=,()11122012101022b b b b b b S ++⋅⋅⋅+=++⋅⋅⋅+=,()21223011122010102224b b b b b b S S ++⋅⋅⋅+=++⋅⋅⋅+=⨯=,∴()230107710501752T S ==-=. 18.命题意图 本题考查频率分布直方图和独立性检验.解析 (Ⅰ)依题意有()1.5 2.5 2.00.80.20.11a +++++⨯=,得 3.0a =.0.350.150.450.250.550.300.650.200.750.080.850.020.537x =⨯+⨯+⨯+⨯+⨯+⨯=.(Ⅱ)依题意作2×2列联表:()221001858121218.36730707030K ⨯⨯-⨯=≈⨯⨯⨯.因为18.367 5.024>,所以有97.5%的把握认为该商品的日销售收入不低于0.6万元与该日是否降价有关. 19.命题意图 本题考查线线垂直的证明,以及点到面距离的求法. 解析(Ⅰ)如图,连接AC ,∵PA PB =,APC PBC ∠=∠,PC PC =,∴PAC PBC ≌△△, ∴90PCA PCB ∠=∠=︒,即PC AC ⊥.∵PC BC ⊥,AC BC C ⋂=,PC ⊥平面ABCD , 又AD ⊂平面ABCD ,∴PC AD ⊥.(Ⅱ)取AB 的中点E ,连接PE ,CE .∵PA PB =,∴PE AB ⊥,由(Ⅰ)知AC BC =,∴CE AB ⊥, ∵PE CE E ⋂=,∴AB ⊥平面PCE ,又AB ⊂平面P AB ,∴平面PAB ⊥平面PCE .过C 作CH PE ⊥于H ,则CH ⊥平面P AB ,由条件知6CH =. 易知PC CE ⊥,设CE m =,则23PE m + 由1122PC CE PE CH ⋅=⋅2633m m =+,得3m =,∴3CE = ∵PD AD ⊥,AD PC ⊥,PC PD P ⋂=,∴AD ⊥平面PCD ,∴AD CD ⊥, 又∵AB CD ∥,∴AD AB ⊥,∴四边形AECD 为矩形,∴3AD CE ==20.命题意图 本题考查导数的几何意义,以及函数与方程的综合问题. 解析(Ⅰ)()222f x x x a '=-+,由题意知()04f a '==-.所以()()()2224212f x x x x x '=--=+-,则当1x <-或2x >时,()0f x '>,当12x -<<时,()0f x '<,所以()f x 的单调递增区间为(),1-∞-和()2,+∞,单调递减区间为()1,2-. (Ⅱ)由()()01f x f =-,得()()010f x f --=, 即()()()323200021113x x a x ⎡⎤⎡⎤-----+--⎡⎤⎣⎦⎣⎦⎣⎦()()()()()20000002111113x x x x x a x =+-+--+++ ()()200011253503x x x a =+-++=. 根据已知,可得方程20025350x x a -++=在区间()0,2内仅有一个实根,设函数()22535g x x x a =-++,其图象的对称轴为()50,24x =∈,所以只需()()()258350,00,20,a g g ∆=-+>⎧⎪>⎨⎪<⎩或0∆=,解得513a -<<-或58a =-,即a 的取值范围是55,138⎛⎫⎧⎫--⋃-⎨⎬ ⎪⎝⎭⎩⎭.21.命题意图 本题考查椭圆方程和定直线的证明. 解析 (Ⅰ)设椭圆C 的焦距为()20c c >,由题意得222222,371019,c a a ba b c ⎧=⎪⎪⎪+=⎨⎪⎪=+⎪⎩,解得229,5,a b ⎧=⎪⎨=⎪⎩∴C 的标准方程为22195x y +=. (Ⅱ)由题可知()3,0A -,()3,0B ,设()11,M x y ,()22,N x y ,则()11,M x y '--,设:MN l x my n =+.联立22,1,95x my n x y =+⎧⎪⎨+=⎪⎩消去x 得()()2225910590m y mny n +++-=,∴1221059mn y y m -+=+,()21225959n y y m -=+,1122,3,3AM BN y k x y k x '⎧=⎪-⎪⎨⎪=⎪-⎩∴()11:33AM y l y x x '=+-,()22:33BN yl y x x =--, 又∵点P 为直线AM '和BN 的交点,∴112233,33,P P P P x y y y x y x y -⎧⋅=+⎪⎪⎨-⎪⋅=-⎪⎩故可得1212332P P x x x y y y ⎛⎫--=+⎪⎝⎭121233P my n my n y y y ⎛⎫+-+-=+ ⎪⎝⎭()121223P y y m n y y y ⎡⎤+=+-⎢⎥⎣⎦()()2102359P mn m n y n ⎡⎤-⎢⎥=+-⋅-⎢⎥⎣⎦, ∴33P P m x y n =+,故3:3OP m l x y n =+. 联立3:,3:,OP MN m l x y n l x my n ⎧=⎪+⎨⎪=+⎩消去y 得3Q x =-,因此,点Q 位于定直线3x =-上.22.命题意图 本题考查极坐标与参数方程.解析 (Ⅰ)()2222164t x t =+,()()22222444t y t -=+, ∴()()()()2222222222216441444t t t y x t t +-++===++, 又22282162244t y t t -==-+>-++, ∴曲线C 的普通方程为()22124y x y +=≠-. (Ⅱ)设P 到l 的距离为d .令cos ,sin ,x y ρθρθ=⎧⎨=⎩得直线l 的直角坐标方程为40x y +-=,设()cos ,2sin P αα,[)0,2απ∈且32πα≠,则d ==1tan 2ϕ=, ∴d的取值范围是22⎡⎢⎣⎦. 23.命题意图 本题考查不等式的证明. 解析 (Ⅰ)由题意知()14,,4111,,4414,.4x x f x x x x ⎧-<-⎪⎪⎪=-≤<⎨⎪⎪≥⎪⎩令()3f x =,得34x =-或34, 结合图象可知()3f x <的解集为3344x x ⎧⎫-<<⎨⎬⎩⎭. (Ⅱ)由题意可知2121a b a b +=++,∴4121121a b -+-=++, ∴41221a b +=++. 令2m a =+,1n b =+,则412m n +=,()()141141333535432222n m a b m n m n m n m n ⎛⎫⎛⎫+=+-=++-=++-≥+-= ⎪ ⎪⎝⎭⎝⎭, 当且仅当23m n ==,即1a =,12b =时等号成立.。
2014/2015学年《人体结构》阶段测试(三)班级姓名学号一、名词解释1.咽峡2. 麦氏点3. 齿状线4.肝门5.腹膜腔6.鼻旁窦7.肺根8.胸膜隐窝二、问答题1.空腹与进食时胆汁输送途径有什么不同?2.请分别说出食管全长三处狭窄的位置及距切牙的距离3.什么是腹膜腔?男、女性腹膜腔有何特点?半卧位或坐位时腹膜腔的最低点在何处?4. 外界空气中的氧经过哪些结构到达血液?二、选择题1.临床上通常把口腔至()的这一段消化管,称上消化道A. 食管B. 胃C. 十二指肠D. 空肠E. 回肠2.大肠不包括A. 盲肠B. 阑尾C. 直肠D. 结肠E. 空肠3.单层柱状上皮分布于()黏膜A. 口腔B. 食管C.小肠D. 肛门E. 咽4.()的肌层为骨骼肌A. 空肠B. 食管上段C. 胃D. 大肠E. 回肠5.口腔与咽的分界标志是A. 腭咽弓B. 腭垂C. 软腭后缘D. 腭咽弓E. 咽峡6.覆盖于牙冠表面的是A. 牙质B. 釉质C. 牙髓D. 牙周膜E. 牙骨质7.恒牙在14岁左右基本出齐,只有()一般在成年后才长出或终身不萌发A. 第3磨牙B. 第3前磨牙C. 尖牙D. 侧切牙E. 第1磨牙8.导管开口于平对上颌第2磨牙处颊黏膜上的是A. 唾液腺 B. 下颌下腺 C. 舌下腺D. 腮腺E. 口腔腺9.导管开口于舌下襞的是A. 唾液腺B. 下颌下腺C. 舌下腺D. 腮腺E. 口腔腺10.腭舌弓与腭咽弓之间有A. 咽扁桃体B. 下颌下腺C. 咽鼓管咽口D. 舌乳头E. 腭扁桃体11.异物易滞留在A. 喉口B. 梨状隐窝C. 咽峡D. 咽鼓管咽口E. 腭舌弓与腭咽弓之间12.第2个狭窄A. 距切牙约15cmB. 在食管与左主支气管交叉处C. 距切牙约40cmD. 在食管穿膈处E. 距切牙约20cm 13.下列关于食管结构特点的描述,错误的是A. 食管腔面有多条纵行黏膜皱襞B. 黏膜上皮为复层扁平上皮C. 食管上段为骨骼肌D. 食管下段为平滑肌E. 外膜为浆膜14.胃底腺的主细胞分泌A. 胃液B. 黏液C. 内因子D. 盐酸E. 胃蛋白酶原15.下列关于胃壁组织结构的描述,错误的是A. 肌层为平滑肌B. 贲门和胃底部的腺体称胃底腺C. 在幽门处,环形肌增厚形成括约肌D. 胃底腺是分泌胃液的主要腺体E. 外膜为浆膜16.十二指肠溃疡的好发部位在A. 十二指肠升部B. 十二指肠降部C. 十二指肠水平部D. 十二指肠空肠曲E. 十二指肠球17.胆总管和胰管共同开口A. 十二指肠升部B. 十二指肠大乳头C. 十二指肠水平部D. 十二指肠空肠曲E. 十二指肠球18.识别空肠起始的标志是A. 幽门B. 十二指肠大乳头C. 回盲瓣D. 十二指肠悬肌E. 十二指肠球19.下列关于小肠的描述,正确的是A. 小肠分为空肠和回肠B. 回肠位于腹腔的左上部 C. 空、回肠之间有明显的界限D. 空肠末端连盲肠E. 小肠黏膜和黏膜下层突向肠腔,形成环行皱襞20.下列关于大肠的描述,不正确的是A. 盲肠是大肠的起始部,位于右髂窝内B. 大肠有三种特征性结构,即结肠带、结肠袋和肠脂垂C. 回盲瓣可阻止大肠内容物逆流到回肠D. 脐与右髂前上棘连线的中、外1/3交点处称麦氏点E. 结肠分为升结肠、横结肠、降结肠和乙状结肠四部分21.肛管内面的结构不包括A. 肛瓣B. 肛窦C. 肛柱D. 直肠壶腹E. 齿状线22. 人体最大的腺体是A. 腮腺B. 胰C.下颌下腺D. 甲状腺E. 肝23. 肝的上界,在右锁骨中线平A. 第3肋B. 第4肋C. 第5肋D. 第6肋E. 第8肋24. 下列关于肝上、下界位置的描述,不确切的是A. 肝的上界,在右锁骨中线平第5肋B. 肝的上界,左锁骨中线平第5肋间隙C. 肝的下界,在右侧与肋弓一致D. 肝的下界,在腹上区可达剑突下1~2cmE. 小儿肝相对较大,肝下界比成人低1~2cm25. 胆囊的分部,不包括A. 胆囊体B. 胆总管C. 胆囊底D. 胆囊颈E. 胆囊管26. Oddi括约肌作用是A. 控制胆汁的排放B. 控制幽门的开放C. 控制胰液的排放D. 可阻止大肠内容物逆流到回肠E. 控制胆汁和胰液的排放27. 被十二指肠包绕的是A. 胰体B. 胰尾C. 胰D. 胰岛E. 胰头28. 下列关于胰岛的描述,错误的是A. 胰岛是胰的内分泌部B. A细胞分泌胰高血糖素C. B细胞分泌胰岛素D. 胰岛分泌胰液E. 胰岛内的B细胞最多29.下列关于腹膜的描述,错误的是A. 腹膜是覆盖于腹、盆壁内面和腹、盆腔脏器表面的一层浆膜 B. 腹膜分为壁腹膜和脏腹膜C. 男性的腹膜腔是密闭的D. 腹膜腔内有少量浆液E. 半卧位或坐位时女性腹膜腔的最低点在膀胱子宫陷凹30.腹膜内位器官不包括A. 盲肠B. 胃C. 肝D. 横结肠E. 空肠31.腹膜间位器官不包括A. 升结肠B. 膀胱C. 子宫D. 阑尾E. 胆囊32.上、下呼吸道的分界器官是A.鼻B.咽C.喉D.气管杈E.以上均不是33.鼻粘膜的易出血区位于A.上鼻甲B.中鼻甲C.下鼻甲D.鼻中隔前下部E.以上均不是34.站立时窦腔内分泌物最不易流出的鼻旁窦是A.额窦B.筛窦C.蝶窦D.上颌窦E.以上均不是35.上呼吸道包括A.口腔、咽、喉B.鼻、咽、喉C.鼻、咽、喉气管D.口腔、鼻、喉、咽、气管E.以上均不是36.喉腔最狭窄的部位在A.喉口B.喉中间腔C.声门裂D.声门下腔E.前庭裂37.成对的喉软骨是A.甲状软骨B.环状软骨C.杓状软骨D.会厌软骨E.以上均不是38.气管切开的常选部位在A.第1~3气管软骨环处B.第2~4气管软骨环处C.第3~5气管软骨环处D.第4~6气管软骨环处E.以上均不是39.喉炎时易引起水肿的部位在A.喉前庭B.喉室C.喉中间腔D.声门下腔E.以上均不是40.左肺A.前缘有心切迹B.有斜裂和水平裂C.可分为三叶D.较右肺粗短E.位于胸腔的纵隔内41.肺下界的体表投影在腋中线处与A.第6肋相交B.第7肋相交C.第8肋相交D.第10肋相交E.以上均不是42.肺下界的体表投影在锁骨中线处与A.第6肋相交B.第7肋相交C.第8肋相交D.第10肋相交E.以上均不是43. 关于阑尾的叙述,正确的是()A. 位于盲肠的下壁B. 为一实质性器官C. 三条结肠带均终止于阑尾根部D. 其根部和末端均较固定E. 长约8~10cm44. 分泌盐酸和内因子的是()A. 贲门腺B. 幽门腺C. 主细胞D. 壁细胞E. 以上均不是45. 肝的基本结构单位()A. 肝细胞B. 肝小叶C. 肝板D. 胆小管E. 肝门管区46. 肝门管区的结构()A. 中央静脉B. 胆小管C. 小叶间动脉D. 肝血窦E. 窦周隙47. 构成小网膜韧带是()A. 镰状韧带B. 肝圆韧带.C. 冠状韧带D. 肝胃韧带E. 胃脾韧带48. 上鼻甲及鼻中隔上部的黏膜称为()A. 呼吸区B. 味觉区C. 出血区D. 嗅区E. 以上均不对49. 肺导气部不包括()A. 段支气管B. 细支气管C. 终末细支气管D. 呼吸性细支气管E. 小支气管50. 能分泌表面活性物质的细胞是()A. 杯状细胞B. Ⅰ型肺泡细胞C. Ⅱ型肺泡细胞D. Ⅰ型肺泡细胞和Ⅱ型肺泡细胞E. 尘细胞。
阶段性测试题四(三角函数与三角形)本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分。
满分150分。
考试时间120分钟。
第Ⅰ卷(选择题 共60分)一、选择题(本大题共12个小题,每小题5分,共60分,在每小题给出的四个选项中,只有一项是符合题目要求的.)1.(2014·威海期中)角α的终边经过点P (sin10°,-cos10°),则α的可能取值为( ) A .10° B .80° C .-10° D .-80°[答案] D[解析] 由条件知tan α=-cos10°sin10°=-tan80°=tan(-80°),故选D.2.(文)(2014·北京海淀期中)在△ABC 中,若tan A =-2,则cos A =( ) A.55B .-55 C.255 D .-255[答案] B[解析] 在△ABC 中,若tan A =-2,则A ∈(π2,π),cos A =-11+tan 2A=-15=-55,故选B.(理)(2014·三亚市一中月考)若tan α=2,则cos2α+sin2α的值为( ) A .0 B.15 C .1 D.54[答案] B[解析] ∵tan α=2,∴cos2α+sin2α=cos 2α-sin 2α+2sin αcos αsin 2α+cos 2α=1-tan 2α+2tan αtan 2α+1=15.3.(文)(2014·江西临川十中期中)已知sin(θ+π2)=35,则cos2θ等于( )A.1225B .-1225C .-725D.725[答案] C[解析] ∵sin(θ+π2)=cos θ=35,∴cos2θ=2cos 2θ-1=-725.(理)(2014·枣庄市期中)化简cos (π+α)cos (π2+α)cos (11π2-α)cos (π-α)sin (-π-α)sin (9π2+α)的结果是( ) A .-1 B .1 C .tan α D .-tan α[答案] C[解析] 原式=-cos α·(-sin α)·(-sin α)-cos α·sin α·cos α=tan α,故选C.4.(2014·山东省菏泽市期中)要得到y =sin(2x -2π3)的图象,只要将函数y =sin(2x +π3)的图象向右平移( )个单位即可( )A.π3 B .π C.2π3 D.π2 [答案] D[解析] ∵sin[2(x -π2)+π3]=sin(2x -2π3),∴只需将y =sin(2x +π3)的图象向右平移π2个单位可得到y =sin(2x -2π3)的图象.5.(2014·九江市七校联考)在△ABC 中,AC =7,∠B =2π3,△ABC 的面积S =1534,则AB =( )A .5或3B .5C .3D .5或6 [答案] A[解析] 设AB =x ,BC =y ,则x >0,y >0,由条件得,⎩⎨⎧72=x 2+y 2-2xy cos 2π3,12xy sin 2π3=1534,即⎩⎪⎨⎪⎧x 2+y 2+xy =49,xy =15, 则⎩⎪⎨⎪⎧ x =3,y =5,或⎩⎪⎨⎪⎧x =5,y =3,∴AB =3或5. 6.(2014·山东省菏泽市期中)已知弧度数为2的圆心角所对的弦长也是2,则这个圆心角所对的弧长是( )A .2B .2sin1C .2sin -11D .sin2[答案] C[解析] 设圆半径为R ,由条件知sin1=1R ,∴R =1sin1,∴l =2R =2sin1,故选C.7.(文)(2014·辽宁师大附中期中)在△ABC 中,角A 、B 均为锐角,且cos A >sin B ,则△ABC 的形状是( )A .直角三角形B .锐角三角形C .钝角三角形D .等腰三角形[答案] C[解析] ∵cos A =sin(π2-A )>sin B,0<π2-A <π2,0<B <π2,∴π2-A >B ,∴A +B <π2,∴C >π2,故选C.(理)(2014·安徽程集中学期中)在△ABC 中,“sin(A -B )cos B +cos(A -B )sin B ≥1”是“△ABC 是直角三角形”的( )A .充分不必要条件B .必要不充分条件C .充分必要条件D .既不充分也不必要条件[答案] A[解析] 由条件式得sin A ≥1,∴sin A =1,∴A 为直角,但△ABC 为直角三角形时,不一定A 为直角,故选A.8.(2014·浙江省五校联考)函数y =2sin(π4-x 2)sin(π4+x2)的图象的一条对称轴为( )A .x =-π2B .x =π2C .x =πD .x =3π2[答案] C[解析] y =2sin(π4-x 2)sin(π4+x 2)=2sin(π4-x 2)cos(π4-x 2)=sin(π2-x )=cos x ,其对称轴方程为x =k π,k ∈Z .9.(文)(2014·江西白鹭洲中学期中)函数y =cos2x 在下列哪个区间上是减函数( ) A .[0,π2]B .[π4,3π4]C .[-π4,π4]D .[π2,π][答案] A[解析] 由2k π≤2x ≤2k π+π得k π≤x ≤k π+π2(k ∈Z ),令k =0知选A.(理)(2014·福州市八县联考)已知ω>0,函数f (x )=sin(ωx +π4)在(π2,π)上单调递减,则ω的取值范围是( )A .[12,54]B .[12,34]C .(0,12]D .(0,2] [答案] A[解析] 由2k π+π2≤ωx +π4≤2k π+3π2及ω>0得,2k πω+π4ω≤x ≤2k πω+5π4ω,k ∈Z . ∵f (x )在(π2,π)上单调递减,∴(π2,π)⊆[2k πω+π4ω,2k πω+5π4ω], ∴k =0,⎩⎨⎧π4ω≤π2,5π4ω≥π.∴12≤ω≤54,故选A. 10.(2014·营口三中期中)函数f (x )=sin(ωx +φ)(ω>0,|φ|<π2)的部分图象如图所示,如果x 1,x 2∈(-π6,π3),且f (x 1)=f (x 2),则f (x 1+x 2)=( )A.12B.22C.32D .1[答案] C[解析] ∵x 1,x 2∈(-π6,π3)时,f (x 1)=f (x 2),∴x 1+x 2=-π6+π3=π6,∴f (x 1+x 2)=f (π6),由图象知,T 2=π3-(-π6)=π2,∴T =2πω=π,∴ω=2,∴f (x )=sin(2x +φ),由于f (x )的图象过点(π12,1),∴sin(π6+φ)=1,∴φ=π3,∴f (π6)=sin(2×π6+π3)=sin 2π3=32,故选C.11.(2014·哈六中期中)2sin 225°-1sin20°cos20°的值为( )A .-1B .-2C .1D .2[答案] B[解析] 原式=-cos50°12sin40°=-2.12.(文)(2014·威海期中)函数f (x )=sin x +cos2x 的图象为( )[答案] B[解析] f (0)=sin0+cos0=1,排除A 、D ;f (-π)=sin(-π)+cos(-2π)=1,排除C ,故选B. (理)(2014·山东省菏泽市期中)函数f (x )=2x -tan x 在(-π2,π2)上的图象大致为( )[答案] C[解析] ∵f (-x )=-2x -tan(-x )=-(2x -tan x )=-f (x ), ∴f (x )为奇函数,排除A 、B ; f ′(x )=(2x -sin x cos x )′=2-1cos 2x ,令f ′(x )≥0得,cos 2x ≥12,∴cos x ≥22或cos x ≤-22, ∵x ∈(-π2,π2),∴-π4≤x ≤π4,故选C.第Ⅱ卷(非选择题 共90分)二、填空题(本大题共4个小题,每小题4分,共16分,把正确答案填在题中横线上.) 13.(2014·华安、连城、永安、漳平、泉港一中、龙海二中六校联考)在△ABC 中,三边a 、b 、c 所对的角分别为A 、B 、C ,若a 2+b 2-c 2+2ab =0,则角C 的大小为________.[答案] 135°[解析] ∵a 2+b 2-c 2+2ab =0, ∴cos C =a 2+b 2-c 22ab =-22,∵0°<C <180°,∴C =135°.14.(文)(2014·甘肃临夏中学期中)函数f (x )=3sin(2x -π3)的图象为C ,则如下结论中正确的序号是________.①图象C 关于直线x =1112π对称;②图象C 关于点(2π3,0)对称;③函数f (x )在区间(-π12,5π12)内是增函数;④由y =3sin2x 的图象向右平移π3个单位长度可以得到图象C .[答案] ①②③[解析] ①当x =11π12时,f (11π12)=3sin 3π2=-3,∴正确;②当x =2π3时,f (2π3)=0,∴正确;③由2k π-π2≤2x -π3≤2k π+π2可得k π-π12≤x ≤k π+5π12,k ∈Z ,∴f (x )的单调递增区间为[k π-π12,k π+5π12](k∈Z ),∴正确;④y =3sin2x 的图象向右平移π3个单位长度得到y =3sin2(x -π3),∴④错误.(理)(2014·威海期中)将函数y =sin(x -π3),x ∈[0,2π]的图象上各点的纵坐标不变横坐标伸长到原来的2倍,再向左平移π6个单位,所得函数的单调递增区间为____________.[答案] [-π6,3π2],[7π2,23π6][解析]由2k π-π2≤12x -π4≤2k π+π2得,4k π-π2≤x ≤4k π+3π2,k ∈Z ,由已知函数中x ∈[0,2π]得所求函数的定义域为[-π6,23π6],令k =0得,-π2≤x ≤3π2,令k =1得,7π2≤x ≤11π2,故所求函数的单调增区间为[-π6,3π2]和[7π2,23π6].15.(文)(2014·吉林省实验中学一模)设α为锐角,若cos(α+π6)=45,则sin(2α+π3)=________.[答案]2425[解析] ∵α为锐角,∴0<α+π6<π,∵cos(α+π6)=45,∴sin(α+π6)=35,∴sin(2α+π3)=2sin(α+π6)·cos(α+π6)=2×35×45=2425.(理)(2014·吉林延边州质检)设△ABC 的三个内角A 、B 、C 所对的三边分别为a 、b 、c ,若△ABC 的面积为S =a 2-(b -c )2,则sin A1-cos A=________.[答案] 4[解析] ∵S =12bc sin A ,a 2-(b -c )2=2bc -(b 2+c 2-a 2)=2bc -2bc cos A ,S =a 2-(b -c )2,∴12bc sin A =2bc -2bc cos A ,∴sin A 1-cos A=4. 16.(2014·浙江省五校联考)已知O (0,0),A (cos α,sin α),B (cos β,sin β),C (cos γ,sin γ),若kOA →+(2-k )OB →+OC →=0(0<k <2),则cos(α-β)的最大值是________.[答案] -12[解析] ∵kOA →+(2-k )OB →+OC →=0,OA →=(cos α,sin α),OB →=(cos β,sin β),OC →=(cos γ,sin γ),∴⎩⎪⎨⎪⎧k cos α+(2-k )cos β+cos γ=0,k sin α+(2-k )sin β+sin γ=0, ∵cos 2γ+sin 2γ=1,∴k 2+(2-k )2+2k (2-k )cos αcos β+2k ·(2-k )sin αsin β=1, ∴cos(α-β)=-2k 2+4k -3-2k 2+4k =1+32k 2-4k , ∵0<k <2,∴-2≤2k 2-4k <0,∴cos(α-β)≤-12.三、解答题(本大题共6个小题,共74分,解答应写出文字说明,证明过程或演算步骤.) 17.(本小题满分12分)(文)(2014·甘肃省金昌市二中期中)已知函数f (x )=2sin x (sin x +cos x ). (1)求f (x )的最小正周期;(2)当x ∈[0,π2]时,求f (x )的最大值.[解析] f (x )=2sin x (sin x +cos x )=2sin 2x +2sin x cos x =1-cos2x +sin2x=2(22sin2x -22cos2x )+1 =2sin(2x -π4)+1,(1)f (x )的最小正周期T =2π2=π.(2)∵0≤x ≤π2,∴-π4≤2x -π4≤3π4,∴当2x -π4=π2,即x =3π8时,f (x )取得最大值,且最大值为f (3π8)=2sin π2+1=2+1.(理)(2014·北京东城区联考)已知函数f (x )=3sin x cos x -cos 2x . (1)求f (x )的最小正周期;(2)当x ∈[0,π2]时,求函数f (x )的最大值及相应的x 的值.[解析] (1)因为f (x )=32sin2x -12cos2x -12=sin(2x -π6)-12,所以T =2π2=π,故f (x )的最小正周期为π.(2)因为0≤x ≤π2,所以-π6≤2x -π6≤5π6.所以当2x -π6=π2,即x =π3时,f (x )有最大值12.18.(本小题满分12分)(文)(2014·辽宁师大附中期中)设△ABC 的内角A ,B ,C 所对的边长分别为a ,b ,c ,且cos B =45,b =2.(1)当A =30°时,求a 的值;(2)当△ABC 的面积为3时,求a +c 的值. [解析] (1)∵cos B =45,∴sin B =35.由正弦定理a sin A =b sin B ,可得a sin30°=103.∴a =53.(2)∵△ABC 的面积S =12ac sin B ,sin B =35,S =3,∴ac =10.由余弦定理b 2=a 2+c 2-2ac cos B 得, 4=a 2+c 2-85ac =a 2+c 2-16,即a 2+c 2=20.∴(a +c )2-2ac =20,(a +c )2=40,∴a +c =210.(理)(2014·威海期中)△ABC 的角A ,B ,C 的对边分别为a ,b ,c ,已知a sin A +b sin B -c sin C =a sin B .(1)求角C ;(2)若a +b =5,S △ABC =323,求c 的值.[解析] (1)根据正弦定理a sin A =b sin B =csin C ,原等式可转化为:a 2+b 2-c 2=ab , ∴cos C =a 2+b 2-c 22ab =12,∵0°<C <180°,∴C =60°.(2)S △ABC =12ab sin C =12ab ·32=332,∴ab =6,c 2=a 2+b 2-2ab ·cos C =(a +b )2-3ab =25-18=7, ∴c =7.19.(本小题满分12分)(2014·江西白鹭洲中学期中)在△ABC 中,a 、b 、c 分别为∠A 、∠B 、∠C 的对边,已知tan A +tan B 1-tan A ·tan B=-3,c =7,三角形面积为332.(1)求∠C 的大小; (2)求a +b 的值.[解析] (1)∵tan(A +B )=tan A +tan B1-tan A tan B =-3,且tan C =tan[π-(A +B )]=-tan(A +B ), ∴tan C =3,又∵0<C <π,∴∠C =π3.(2)由题意可知:S △ABC =12ab sin C =12ab sin π3=34ab =332,∴ab =6.由余弦定理可得:c 2=a 2+b 2-2ab cos C =(a +b )2-3ab , ∴(a +b )2=3ab +c 2=3×6+(7)2=25, 又a >0,b >0,∴a +b =5.20.(本小题满分12分)(文)(2014·马鞍山二中期中)已知A ,B ,C 的坐标分别为A (3,0),B (0,3),C (cos α,sin α),α∈(π2,3π2).(1)若|AC →|=|BC →|,求角α的值;(2)若AC →·BC →=-1,求2sin 2α+sin2α1+tan α的值. [解析] (1)∵AC →=(cos α-3,sin α),BC →=(cos α,sin α-3),∴AC →2=(cos α-3)2+sin 2α=10-6cos α,BC →2=cos 2α+(sin α-3)2=10-6sin α,由|AC →|=|BC →|,可得AC →2=BC →2,即10-6cos α=10-6sin α,得sin α=cos α.又∵α∈(π2,3π2),∴α=5π4. (2)由AC →·BC →=-1,得(cos α-3)cos α+sin α(sin α-3)=-1,∴sin α+cos α=23.① 又2sin 2α+sin2α1+tan α=2sin 2α+2sin αcos α1+sin αcos α=2sin αcos α. 由①式两边分别平方,得1+2sin αcos α=49, ∴2sin αcos α=-59.∴2sin 2α+sin2α1+tan α=-59. (理)(2014·辽宁师大附中期中)已知向量a =(2sin x ,sin x -cos x ),b =(cos x ,3(cos x +sin x )),函数f (x )=a ·b +1.(1)当x ∈[π4,π2]时,求f (x )的最大值和最小值; (2)求f (x )的单调区间.[解析] (1)f (x )=sin2x -3cos2x +1=2sin(2x -π3)+1. ∵π4≤x ≤π2,∴π2≤2x ≤π,∴π6≤2x -π3≤2π3, ∴12≤sin(2x -π3)≤1,∴1≤2sin(2x -π3)≤2, 于是2≤2sin(2x -π3)+1≤3, ∴f (x )的最大值是3,最小值是2.(2)由2k π-π2≤2x -π3≤2k π+π2,k ∈Z 得2k π-π6≤2x ≤2k π+5π6,k ∈Z , ∴k π-π12≤x ≤k π+5π12,k ∈Z , 即f (x )的单调递增区间为[k π-π12,k π+5π12],k ∈Z , 同理由2k π+π2≤2x -π3≤2k π+3π2,k ∈Z 得,f (x )的单调递减区间为[k π+5π12,k π+11π12],k ∈Z . 21.(本小题满分12分)(2014·马鞍山二中期中)如图A 、B 是海面上位于东西方向相距5(3+3)n mile 的两个观测点,现位于A 点北偏东45°,B 点北偏西60°的D 点有一艘轮船发出求救信号,位于B 点南偏西60°且与B 点相距203n mile 的C 点的救援船立即前往营救,其航行速度为30n mile/h ,该救援船到达D 点需要多长时间?[解析] 由题意知AB =5(3+3)n mile ,∠DBA =90°-60°=30°,∠DAB =90°-45°=45°, ∴∠ADB =180°-(45°+30°)=105°,在△DAB 中,由正弦定理得,DB sin ∠DAB =AB sin ∠ADB∴DB =AB ·sin ∠DAB sin ∠ADB=5(3+3)·sin45°sin105°=5(3+3)·sin45°sin45°·cos60°+sin60°·cos45°=53(3+1)3+12=103(n mile). 又∠DBC =∠DBA +∠ABC =30°+(90°-60°)=60°,BC =203(n mile),在△DBC 中,由余弦定理得,CD 2=BD 2+BC 2-2BD ·BC ·cos ∠DBC =300+1200-2×103×203×12=900, ∴CD =30(n mile),则需要的时间t =3030=1(h). 答:救援船到达D 点需要1h.22.(本小题满分14分)(文)(2014·安徽程集中学期中)已知函数f (x )=A cos(ωx +φ)(A >0,ω>0,0<φ<π2)的图象过点(0,12),最小正周期为2π3,且最小值为-1.(1)求函数f (x )的解析式;(2)若x ∈[π6,m ],f (x )的值域是[-1,-32],求m 的取值范围. [解析] (1)由函数的最小值为-1,可得A =1,因为最小正周期为2π3,所以ω=3.可得f (x )=cos(3x +φ),又因为函数的图象过点(0,12),所以cos φ=12,而0<φ<π2,所以φ=π3,故f (x )=cos(3x +π3). (2)由x ∈[π6,m ],可知5π6≤3x +π3≤3m +π3,因为f (π6)=cos 5π6=-32,且cosπ=-1,cos 7π6=-32, 由余弦曲线的性质知,π≤3m +π3≤7π6,得2π9≤m ≤5π18,即m ∈[2π9,5π18]. (理)(2014·浙江省五校联考)已知函数f (x )=(3sin ωx +cos ωx )cos ωx -12,其中ω>0,f (x )的最小正周期为4π.(1)求函数f (x )的单调递增区间;(2)在△ABC 中,角A 、B 、C 的对边分别是a 、b 、c ,且满足(2a -c )cos B =b cos C ,求函数f (A )的取值范围.[解析] f (x )=3sin ωx ·cos ωx +cos 2ωx -12=32sin2ωx +12cos2ωx =sin(2ωx +π6). (1)∵2π2ω=4π,∴ω=14,f (x )=sin(x 2+π6). 由2k π-π2≤x 2+π6≤2k π+π2(k ∈Z )得: 4k π-4π3≤x ≤4k π+2π3. ∴f (x )的单调递增区间是[4k π-4π3,4k π+2π3](k ∈Z ). (2)由正弦定理得,(2sin A -sin C )cos B =sin B ·cos C ,∴2sin A cos B =sin(B +C ),∵sin(B +C )=sin(π-A )=sin A >0,∴cos B =12,∵0<B <π,∴B =π3, ∴0<A <2π3,π6<A 2+π6<π2,∴f (A )∈(12,1).。
学校 班级 姓名 考号________________考试时间 ______ ________ 装订线内不要答题◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆装◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆订◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆线◆◆◆◆◆◆◆◆ 2014--2015学年度七年级数学练习七十一 第三次阶段性测试模拟(四) 本试卷共印7个班:初一8、9、10、11、12、14、15, 命题人:尹东泽 时间:2014-12-11 一、 选择题(下列各题只有一个正确答案,每题3分,共30分) 题号 1 2 3 4 5 6 7 8 答案 1、下列式子中,正确的是( ) A .55-=- B .55-=- C .10.52-=- D .1122--= 2、实数a 、b 在数轴上的位置如图所示,则下列式子成立的是( ) A .a +b>0 B .a >-b C .a +b<0 D .-a <b 3、右图表示一个由相同小立方块搭成的几何体的俯视图,小正方形中的数字表示该位置上小立方块的个数,那么该几何体的主视图为( ) 4、在数轴上与原点的距离等于2个单位的点表示的数是( ) A .2 B .-2 C .-1和3 D .-2和2 5.下列运算中,正确的是( ) A .b a b a b a 2222=+- B .22=-a a C .422523a a a =+ D .ab b a 22=+ 6.国家规定:存款利息税=利息×20%,银行一年定期储蓄的年利率为 1.98%.小明有一笔一年定期存款,如果到期后全取出,可取回1219元。
若设小明的这笔一年定期存款是x 元,则下列方程中正确的是( ) A .1219%20%98.1=⋅+x B .1219%20%98.1=⋅x C.1219%)201(%98.1=-⋅x D .1219%)201(%98.1=-⋅+x x 卷面分7.如果a+b>0,且ab<0,那么( )A 。
河南十所名校2014-2015学年高中毕业班阶段性测试(三)物 理本试题卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分。
考生作答时,将答案答在答题卡上(答题注意事项见答题卡),在本试题卷上答题无效。
考试结束后,将本试题卷和答题卡一并交回。
第Ⅰ卷 选择题一、选择题:本题共10小题,每小题5分,共50分。
第1-6题只有一个选项符合题目要求,第7-10题有多个选项符合题目要求,全部选对的得5分,选对但不全的得3分,有选错的得0分。
1.质点沿x 轴运动的v -t 图像如图所示,规定向右为正方向,t =8s 时质点位于x =0 m 的位置,则t =0时质点位于A .x =8mB .x =6mC .x =4mD .x =2m2.在玻璃皿的中心放一个圆柱形电极B ,沿边缘内壁放一个圆环形电极A ,把A 、B 分别与 电源的两极相连,然后在玻璃皿中放入导电液体。
现把玻璃皿放在如图所示的磁场中,液体就会旋转起来。
若从上向下看,下列判断正确的是A .A 接电源正极,B 接电源负极,液体顺时针旋转B .A 接电源负极,B 接电源正极,液体顺时针旋转C .A 、B 与50 Hz 的交流电源相接,液体持续旋转D .仅磁场N 、S 极互换后,重做该实验发现液体旋转方向不变3.经过探究,某同学发现:点电荷和无限大的接地金属平板间的电场(如图甲所示)与等量异种点电荷之间的电场分布(如图乙所示)完全相同。
图丙中点电荷q 到MN 的距离OA 为L ,AB 是以电荷q 为圆心、L 为半径的圆上的一条直径,则B 点电场强度的大小是A .2109kq L B .2kq L C .289kq L D .234kq L4.如图甲所示,在木箱内粗糙斜面上静止一个质量为m的物体,木箱竖直向上运动的速度v与时间t的变化规律如图乙所示,物体始终相对斜面静止。
斜面对物体的支持力和摩擦力分别为N和f,则下列说法正确的是A.在0~t1时间内,N增大,f减小B.在0~t1时间内,N减小,f增大C.在t1~t2时间内,N增大,f增大D.在t1~t2时间内,N减小,f减小5.在光滑绝缘的水平面上.OP右侧有如图所示的匀强磁场,两个相同的带电小球a和b以大小相等的初速度从O点沿垂直磁场方向进入匀强磁场,最后两球均运动到OP边界的P侧,下列说法正确的是A.球a带正电,球b带负电B.球a在磁场中运动的时间比球b的短C.球a在磁场中运动的路程比球b的短D.球a在OP上的落点与O点的距离比球b的近6.如图甲所示,轻杆一端与质量为1 kg、可视为质点的小球相连,另一端可绕光滑固定轴在竖直平面内自由转动。
1.(2014重庆一中高三下学期第一次月考,6)已知一个四面体的一条棱长为,其余棱长均为2,则这个四面体的体积为()(A)1 (B)(C)(D)3[解析] 1. 取边长为的边的中点, 并与其对棱的两个端点连接,2.(2014重庆一中高三下学期第一次月考,5)某几何体的三视图如下图所示,则它的表面积为()(A)(B)(C)(D)[解析] 2. 该三视图对应的几何体为组合体,其中上半部为半径为3母线长为5的圆锥,下半部为底面半径为3高为5的圆柱,所以其表面积为.3.(2014天津蓟县第二中学高三第一次模拟考试,5) 某几何体的三视图如图所示,根据图中标出的数据.可得这个几何体的表面积为( )A.B.C.D. 12[解析] 3. 从三视图中可以看出该几何体是正四棱锥,且其斜高为底面是边长为2的正方形,故其表面积为.4. (2014山西忻州一中、康杰中学、临汾一中、长治二中四校高三第三次联考,11) 三棱锥P—ABC的四个顶点均在同一球面上,其中△ABC是正三角形,PA⊥平面ABC,PA=2AB=6,则该球的体积为( )[解析] 4. 三棱锥P-ABC的外接球与高为6底面边长为3的正三棱柱的外接球相同,即可把三棱锥P-ABC补成高为6底面边长为3的正三棱柱,由此可得球心O到底面ABC的距离为3,设底面ABC的外接圆圆心为O1, 连接OA, O1A、OO1, 则O1A =, OO1=3,所以OA2=O1A2+=,所以该求的体积为.5. (2014山西忻州一中、康杰中学、临汾一中、长治二中四校高三第三次联考,3) 下图是一个体积为10的空间几何体的三视图,则图中x的值为( )A. 2B. 3C. 4D. 5[解析] 5. 根据三视图可知,该几何体由两部分组成,上半部为底面边长分别为3和2的长方形高为x的四棱锥,下半部为高为1底面边长分别为3和2的长方形的长方体,所以其体积为,解得x=2.6. (2014山西太原高三模拟考试(一),10) 在三棱锥S-ABC中,AB⊥BC, AB=BC= ,SA=SC=2,二面角S-AC-B的余弦值是 , 若S、A、B、C都在同一球面上,则该球的表面积是( )[解析] 6. 取线段AC的中点E, 则由题意可得SE⊥AC, BE⊥AC, 则∠SEB即为二面角S-AC-B的平面角, 在△SEB中, SE=, BE=1, 根据余弦定理, 得, 在△SAB和△SCB中, 满足勾股定理, 可得SA⊥AB, SC⊥BC, 所以S、A、B、C都在同一球面上,则该球的直径是SB, 所以该球的表面积为.7. (2014山西太原高三模拟考试(一),8) 一个几何体的三视图如图所示(单位:cm),则该几何体的体积为( )A. (32+ ) ㎝3B. (32+ ) ㎝3C. (41+ ) ㎝3D. (41+ ) ㎝3[解析] 7. 该三视图对应的几何体为由上中下三部分构成的组合体,其中上半部是长宽高分别为3、3、1的长方体;中半部为底面直径为1高为1的圆柱;下半部为长宽高分别为4、4、2的长方体,其体积为.8.(2014安徽合肥高三第二次质量检测,3) 某空间几何体的三视图如图所示,则该几何体的体积为()A.B.C.D. [[解析] 8. 由三视图知,原几何体是一个三棱柱,底面是等腰直角三角形,且腰长为2,所以该三棱柱的体积.9. (2014重庆杨家坪中学高三下学期第一次月考,6) 已知某几何体的三视图如图所示,若该几何体的体积为24,则该几何体的底面积是()A. 6B. 12C. 18D. 24[解析] 9. 根据三视图可知,该几何体是一个有一条侧棱垂直于底面的四棱锥,该四棱锥的高为4,因为体积为24,所以底面积.10. (2014河北石家庄高中毕业班复习教学质量检测(二),8) 点, ,,在同一个球的球面上,,, 若四面体体积的最大值为 , 则该球的表面积为( )[解析] 10. 如图,当平面时,四面体体积的最大. 此时,,所以,设球半径为R,则,即,从而,故.11. (2014湖北黄冈高三4月模拟考试,6) 一个几何体的三视图如图所示,其中正视图是正三角形,则几何体的外接球的表面积为()A.B.C.D.[解析] 11.原几何体如图中三棱锥,由已知正视图、侧视图和俯视图均是三角形,可知该几何体有一个侧面垂直于底面,高为,底面是一个等腰直角三角形,则这个几何体的外接球的球心在高线上,且是等边三角形的中心,所以这个几何体的外接球的半径为,所以这个几何体的外接球的表面积为.12. (2014河北唐山高三第一次模拟考试,9) 正三棱锥的高和底面边长都等于6,则其外接球的表面积为()A.B.C.D.[解析] 12. 设球半径为,如图所示,可得,解得,所以表面积为.13. (2014河北唐山高三第一次模拟考试,7) 某几何体的三视图如图所示,则该几何体的体积为()A. 6B. 2C. 3D.[解析] 13. 由三视图知,原几何体的体积为.14. (2014贵州贵阳高三适应性监测考试, 5) 下图是一个几何体的三视图,则该几何体的体积等于()[解析] 14.该几何体是一三棱柱,qi 其体积为=4.15. (2014黑龙江哈尔滨第三中学第一次高考模拟考试,8) 如图所示,是一个空间几何体的三视图,且这个空间几何体的所有顶点都在同一个球面上,则这个球的表面积是()A. B. C. D.[解析] 15. 由三视图知,原几何体是一个三棱柱,其底边为边长为2的等边三角形,高为2,所以球心在三棱柱上下两底面的中心的连线的中点,球的半径为,球的表面积为.16.(2014山东潍坊高三3月模拟考试数学(理)试题,7)三棱锥S-ABC的所有顶点都在球O的表面上,SA平面ABC,AB BC,又SA=AB= BC=1,则球O的表面积为( )(A) (B)(C) 3 (D) 12[解析] 16. 三棱锥S-ABC的外接球与高为1底面边长为1等腰直角三角形的直三棱柱的外接球相同,即可把三棱锥P-ABC补成高为1底面边长为1等腰直角三角形的直三棱柱,由此可得球心O到底面ABC的距离为,设底面ABC的外接圆圆心为O1, 连接OA, O1A、OO1, 则O1A =, OO1=,所以OA2=O1A2+=,所以该求的体积为.17.(2014吉林实验中学高三年级第一次模拟,8)若某棱锥的三视图(单位:cm) 如图所示,则该棱锥的体积等于()A.10 cm3 B.20 cm3C.30 cm3 D.40 cm3[解析] 17. 根据三视图可知,该几何体为如下图所示的四棱锥,其中PA⊥PB,底面ABCD 为矩形且与侧面PAB垂直,过点P作线段AB的垂线,则该垂线即为四棱锥的高,其长度为cm,而矩形ABCD的边长AD=5,AB=5,所以其体积为 cm3.18.(2014湖北八校高三第二次联考数学(理)试题,4)已知某几何体的三视图(单位:cm)如图所示,则该几何体的体积是()A.48cm3 B.98cm3C.88cm3 D.78cm3[解析] 18. 该三视图对应的几何体为长、宽、高分别为6 cm、3 cm、6 cm的长方体截去一个三棱锥后所得的几何体,其体积为6×3×6-98 cm3.19.(2014河南豫东豫北十所名校高中毕业班阶段性测试(四)数学(理)试题, 11) 如图所示,棱长为6的正方体无论从哪一个面看,都有两个直通的边长为l的正方形孔,则这个有孔正方体的表面积(含孔内各面)是( )( A) 222 (B) 258 (C) 312 (D) 324[解析] 19. 表面积等于正方体的表面积减去12个表面上的小正方形面积,加上6个棱柱的侧面积,减去6个通道的6个小正方体的表面积.则S=6×36-12+6×4×6-6×6=312.故选C.20.(2014河南豫东豫北十所名校高中毕业班阶段性测试(四)数学(理)试题, 4) 某几何体的三视图如图所示,其中正视图与侧视图均为矩形,俯视图上半部分为半,圆,则该几何体的体积为( )(A) (B) (C)(D)[解析] 20. 根据三视图可知,该几何题是由半圆柱和直三棱柱构成的组合体,其中半圆柱的底面半径为1,高为2;直三棱柱的底面是腰长为的等腰直角三角形,故该几何体的体积为.21.(2014吉林省长春市高中毕业班第二次调研测试,9) 某几何体的三视图如图所示,则它的表面积为()A.B.C. D.[解析] 21. 由几何体的三视图可知,该几何体是一个沿旋转轴作截面,截取的半个圆锥,底面半径是1,高是2,所以母线长为,所以其表面积为底面半圆面积和圆锥的侧面积的一半以及截面三角形的面积的和,即,故选.22.(2014湖北武汉高三2月调研测试,8) 如图,在长方体ABCD-A1B1C1D1中,E,H分别是棱A1B1,D1C1上的点(点E与B1不重合),且EH∥A1D1,过EH的平面与棱BB1,CC1相交,交点分别为F,G.设AB=2AA1=2a.在长方体ABCD-A1B1C1D1内随机选取一点,记该点取自于几何体A1ABFE-D1DCGH内的概率为P,当点E,F分别在棱A1B1,BB1上运动且满足EF=a时,则P的最小值为[解析] 22. 根据几何概型,===,其中“=” 当且仅当时成立. 故选D.23. (2014吉林高中毕业班上学期期末复习检测, 7) 某几何体的三视图(如图),则该几何体的体积是()A.B.C.D.[解析] 23. 由三视图知,原几何体是由一个半圆柱与一个半圆锥构成,其体积为.24. (2014河南郑州高中毕业班第一次质量预测, 4) 如图,某几何体的正视图和俯视图都是矩形,侧视图是平行四边形,则该几何体的表面积为()A.B.C.D.[解析] 24.由已知,元几何体为四棱柱,其底面边长为,侧视图的高为,底面积为,又因为棱柱的高为3,侧面积为,故原几何体的表面积为.25. (2014河北衡水中学高三上学期第五次调研考试, 3) 一个几何体按比例绘制的三视图如图所示(单位:), 则该几何体的体积为().A. B. C. D.[解析] 25.由三视图可知,该几何体是由三个棱长为1的正方体加半个正方体构成,所以体积为26.(2014成都高中毕业班第一次诊断性检测,8) 一个长方体被一个平面截去一部分后所剩几何体的三视图如下图所示(单位:cm) ,则该几何体的体积为()(A) 120 (B) 80 (C) 100 (D) 60[解析] 26.画出直观图可知,原几何体的体积.27. (2014北京东城高三12月教学质量调研) 一个空间几何体的三视图如图所示,则该几何体的体积为()(A)(B)(C)(D)[解析] 27. 原几何体是由一个圆柱与一个圆锥构成,其体积为..(2014天津蓟县邦均中学高三第一次模拟考试,13) 如果一个几何体的三视图如图所示(单位长度: cm), 则此几何体的表面积是。
天一大联考(原豫东、豫北十所名校联考) 2014-2015学年高中毕业班阶段性测试(三)数学(理科)本试题卷分第I 卷(选择题)和第H 卷(非选择题)两部分考生作答对,将答案答在答题卡上(答题注意事项见答题卡),在本试题卷上答题无效考试结束后,将本试题卷和答题卡一并交回第I 卷一、选择题:本大题共12小题,每小题5分在每小题给出的四个选项中,只有一项是符合题目要求的(1)已知全集U=R ,集合 {}{}2|02,|0A x x B x x x =≤≤=->,则图中的阴影部分表示的集合为(A)(-∞,1]U(2,+∞) (B) ()(),01,2-∞(C)[1,2) (D)(1,2] (2)已知i 是虚数单位,则复数213(1)ii -++在复平面内所对应的点位于 (A)第四象限 (B)第三象限 (C)第二象限 (D)第一象限(3)已知数列 {}n a 的通项为 22n a n n λ=-,,则“ 0λ<”是“ 1,n n n N a a *+∀∈>”的 (A)充分不必要条件 (B)必要不充分条件(C)充要条件 (D)既不充分也不必要条件(4)已知圆 222:(1)C x y r ++=与抛物线 2:16D y x =的准线交于A ,B 两点,且 8AB =,则圆C 的面积为( A)5 π (B)9π (C)16π (D)25 π(5)已知 ()f x 是定义在R 上的奇函数,且当x>0对, 2cos ,08,()6log ,8,xx f x x x π⎧<≤⎪=⎨⎪>⎩((16))f f -=(A) 12-(B)32- (C)12 (D) 32(6)高三某班上午有4节课,现从6名教师中安排4人各上一节课如果甲、乙两名教师不上第一节课,丙必须上最后一节课,则不同的安排方案种数为( A)36 (B)24 (C)18 (D)12 (7)设 331sin(810),tan(),lg 85a b c π=-==,则它们的大小关系为 (A)a<b<c (B)a<c<b (C)b<c<a (D)c<a<b(8)函数 33()xx f x e-=的大致图象是(9)如图的几何体是长方体 1111ABCD A B C D -的一部分,其中 113,2AB AD DD BB cm ====则该几何体的外接球的表面积为(A 211cm π (B) 222cm π(C)211223cm ( D)21122cm π (10)执行如图所示的程序框图,输出的S 为 (A)1 006 (B)1 007 ( C)1 008 (D)1 009(11)双曲线 2222:1(0,0)x y C a b a b-=>>的一条渐近线与直线X+2y +1 =0垂直, 12,F F 为C 的焦点A 为双曲线上一 点,若 122F A F A =,则 21cos AF F∠= (A) 32 (B) 54 ( C) 55(D)14(12)设 ()ln f x x =,若函数 ()()g x f x ax =-在区间(0,4)上有三个零点,则实数a 的 取值范围是(A) 10,e ⎛⎫ ⎪⎝⎭ (B) l n 2,2e ⎛⎫⎪⎝⎭ ( C) l n 21,2e ⎛⎫⎪⎝⎭ (D) l n 20,2⎛⎫⎪⎝⎭第Ⅱ卷二、填空题:本大题共4小题,每小题5分(13)设 2010sin n xdx π=⎰,则 31nx x ⎛⎫- ⎪⎝⎭展开式中的常数项为_________(用数字作答) (14某天,小赵、小张、小李、小刘四人一起到电影院看电影,他们到达电影院之后发现,当天正在放映A ,B ,C ,D ,E 五部影片于是他们商量一起看其中的一部影片: 小赵说:只要不是B 就行; 小张说:B ,C ,D ,F 都行;小李说:我喜欢D ,但是只要不是C 就行; 小刘说:除了E 之外,其他的都可以据此判断,他们四人可以共同看的影片为____(15)△ABC 中, 2,1,120AB AC BAC ==∠=,若 2BD DC =,则 AD BC ⋅= =______________.(16)已知数列 {}n a 的各项取倒数后按原来顺序构成等差数列,各项都是正数的数列 {}n x满足 11233,39,x x x x =++=. 1211n nn a a an n n x x x ++++==,则 n x =__________.三、解答题:解答应写出文字说明,证明过程或演算步骤 (17)(本小题满分10分)已知向量 2(3sin,1),(cos ,cos )444x x xm n ==,记 ()f x m n =⋅ (I)若 3()2f a =,求 2cos()3a π-的值; (Ⅱ)将函数 ()y f x =的图象向右平移 23π个单位得到 ()y g x =的图象,若函数()y g x k =-在 70,3π⎡⎤⎢⎥⎣⎦上有零点,求实数k 的取值范围(18)(本小题满分12分)设等差数列 {}n a 的前n 项和为 n S , 561124,143a a S +==数列 {}n b 的前n 项和为n T 满足112(1)()n a n T a n N λ-*=--∈(I)求数列 {}n a 的通项公式及数列 11n n a a +⎧⎫⎨⎬⎩⎭的前n 项和;(Ⅱ)是否存在非零实数 λ,使得数列 {}n b 为等比数列?并说明理由 (19)(本小题满分12分)已知国家某5A 级大型景区对每日游客数量拥挤等级规定如下表:该景区对3月份的游客量作出如图的统计数据:(I)某人3月份连续2天到该景区游玩,求这2天他遇到的游客拥挤等级均为良的概率; (Ⅱ)从该景区3月份游客人数低于10 000人的天数中随机选取3天,记这3天游客拥挤等级为优的天数为ξ,求ξ的分布列及数学期望(20)(本小题满分12分)如图,在四棱锥P -ABCD 中,AD ⊥DB ,其中三棱锥P- BCD 的三视图如图所示,且3s i n5B DC ∠=(I)求证:AD ⊥PB(Ⅱ)若PA 与平面PCD 所成角的正弦值为 121365,求AD 的长 (21)(本小题满分12分)已知椭圆 2222:1(0)x y E a b a b +=>>)过点 2(1,)2Q -,且离心率 22e =,直线 l 与E 相交于M ,N 两点,l 与x 轴、y 轴分别相交于C ,D 两点,0为坐标原点(I)求椭圆E 的方程:(Ⅱ)判断是否存在直线l ,满足 2,2OC OM OD OD ON OC =+=+?若存在,求出直 线 l 的方程;若不存在,说明理由 :22)(本小题满分12分) 设函数 (),ln bxf x ax e x=-为自然对数的底数 (I)若函数f(x)的图象在点 22(,())e f e 处的切线方程为 2340x y e +-=,求实数a ,b 的值;(Ⅱ)当b=l 时,若存在 212,,x x e e ⎡⎤∈⎣⎦,使 12()'()f x f x a ≤+成立,求实数a 的最小值- 11 -。
四川省营山县回龙中学2014-2015学年高二6月阶段测试语文试卷考试时间:150分钟;满分:150分第I卷(选择题)一、语言基础知识(15分)1.下列各组词语中,画线字读音全都正确的一项是A.百舸(kē)霎时(shà)内帏(wéi)叱咤风云(zhà)B.盥洗(guàn)韶光(sháo)驯熟(xùn)畏葸(xǐ)不前C.瘦削(xuē)聒噪(guā)脸颊(jiá)旁稽博采(jī)D.朱拓(tà)估量(liáng)广袤(máo)卓有成效(zhuó)2.下列各组词语中,没有错别字的一组是A.洽谈坐落雷厉风行出奇不意B.扫瞄陷阱谈笑风生别出心裁C.通缉疏浚纷至沓来彪炳千古D.流弊杜撰张灯结彩彬彬有理3.下列各句中,画线的成语使用恰当的一项是A.朴实的莫言在公众场合表现出的谦逊赢得了大众对他的敬重。
他的微博中,满是热心粉丝的溢美之词。
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”这个谚语告诉我们:做任何事情都不能大而化之。
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天一大联考(原豫东、豫北十所名校联考)2014—2015学年高中毕业班阶段性测试(二)生物·答案1~20题,每小题2分,共40分。
1.B2.B3.B4.D5.D6.C7.D8.C9.A 10.D 11.C 12.B 13.C 14.B 15.B 16.D 17.B 18.C 19.A 20.A21.(除注明外,每空1分,共10分)(1)核糖体高尔基体(2)细胞质基质的pH高于溶酶体,导致水解酶活性降低(2分)(3)抑癌阻止细胞不正常的增殖核糖体、中心体、线粒体(2分)(4)0 内质网22.(除注明外,每空1分,共10分)(1)光照强度和二氧化碳浓度(2分)光照强度(2)遮光(或黑暗)(3)单位时间内产生的气泡数温度主要通过影响酶的活性进而影响光合作用强度(2分)(4)25 18(5)细胞质基质23.(除注明外,每空1分,共10分)(1)促进rbcS基因和cab基因的转录光反应(2)②④起始密码和终止密码(3)细胞核、叶绿体(2分)细胞核和细胞质(4)叶绿素(或叶绿素a和叶绿素b)用药物抑制核基因的表达,检测叶绿体中是否有DNA聚合酶的合成(2分)24.(除注明外,每空1分,共9分)(1)2 4(2)能合成不能合成(两个答案位置可互换)(3)9∶7(2分)(4)Ⅱ2(5)X D Y d X d Y D(两个答案位置可互换)25.(除注明外,每空1分,共11分)(1)细菌细胞吸水过多,细胞膜过度膨胀发生破裂(2分)(2)S型和R(3)用注射法,通过观察小鼠的生活情况来区分(2分)(4)①核酸(或DNA)水解荚膜 DNA(或控制荚膜合成的基因)(5)转录翻译。